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Tain Royal Academy Higher Grade Physics Unit 1 Question booklet 1.1 Vectors 1.2 Equations of Motion 1.3 Newton’s second law, Energy and Power 1.4 Momentum and impulse 1.5 density and pressure 1.6 Gas Laws

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Tain Royal Academy

Higher Grade Physics

Unit 1

Question booklet

1.1 Vectors 1.2 Equations of Motion 1.3 Newton’s second law, Energy and Power 1.4 Momentum and impulse 1.5 density and pressure 1.6 Gas Laws

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Contents

Page number Revision of speed an acceleration 3 1.1 Vectors Vector and scalers 5 Past exam Questions: vector & scaler 7 Adding Force Vectors 8 Components 10 Past exam question: vector anaylsis 12 1.2 Equations of Motion Graphs of Motion 16 Past exam questions:graphs of motion 20 Equations of Motion 27 Past exam questions:equations of motion 29 Projectiles 34 Past exam questions:projectiles 36 1.3 Newton’s second law, Energy and power Revision of force, work and energy 40 Past exam paper questions: Energy 42 Force and acceleration 43 Past exam questions:forces 47 Past exam questions:forces on a slope 50 1.4 Momentum and Impulse Momentum 53 Past exam questions: momentum 56 Impulse 62 Past exam questions: impulse 64 1.5 Density & Pressure Density 68 Past exam question: Density 69 Pressure 70 Pressure in liquids 71 Past exam questions: Pressure 73 Past exam questions: Upthrust and pressure in a liquid 77 1.6 Gas laws Pressure and Volume (constant temperature) 79 Pressure and Temperature (constant volume) 81 Temperature and Volume (constant pressure) 82 General gas equation 83 Past exam questions: Gas laws 84

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Revision of Speed and Acceleration 1. What is meant by average speed? 2. How would you measure the average speed of a bicycle? 3. If you want to reach Edinburgh (290km away) in 3 hours, what must be your average speed? Why

would you need to travel faster than that speed at some stages of your journey? 4. It takes 2.5 hours to fly from Inverness to Southampton at an average speed of 370kmh-1. How far is

Southampton from Inverness? 5. How long will it take a walker to cover 1500m at a speed of 3.5ms-1? 6. An athlete runs 800m in 1minute 53 seconds. What is her average speed? 7. A snail moves at a speed of 0.001ms-1. How far will it travel in 1 hour? 8. In orbit, a spacecraft takes 80 minutes to orbit the earth once, a distance of 50,800km. What is the

speed of the spacecraft? 9. What is meant by instantaneous speed? 10. Describe how you would measure the instantaneous speed of a trolley near the bottom of a runway. 11. A hand operated digital stopwatch is suitable for measuring the average speed of a runner, but should

not be used to measure the instantaneous speed. Explain why not. 12. The following is a record of a journey using public transport.

(a) How long did the journey take?

(b) How far was the journey?

(c) What was the average speed? 13. A car’s motion is described in the

graph shown below.

(a) What is the car’s average speed over the 12 seconds?

(b) What is its instantaneous speed at 8.0s?

(i) 1.0km at 4.0kmh-1, walking (ii) 10 minute wait (iii) 32km at 48kmh-1, by bus (iv) 45 minute wait

(v) 2400km at 800kmh-1, by plane

(vi) 30 minute wait (vii) 50km at 100kmh-1, by coach (viii) 20 minute wait

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14. What is meant by acceleration? Write down the formula used to calculate acceleration and explain what the symbols mean.

15. Describe how you would measure the acceleration of a vehicle. 16. A car is travelling at 8.0ms-1 and accelerates to 24ms-1 in 4.0 seconds. What is its acceleration?

17. An archer releases an arrow and it attains a speed of 50ms-1 having accelerated at 400ms-2. How long did the acceleration take?

18. A lorry brakes with an acceleration of -4.5ms-2 and takes 10 seconds to reduce its speed to 10ms-1. What was its initial speed?

19. A plane is flying at a speed of 250ms-1 and accelerates for 8 seconds at 6.7ms-2. What is its final speed?

20. Sketch a speed-time graph for each of the following motions.

(a) Steady speed.

(b) Speeding up uniformly.

(c) Slowing down uniformly.

21. Use the graph to find the following.

(a) The acceleration between C and D

(b) The deceleration between A and B

(c) Distance travelled in the first 4 seconds.

(d) Distance travelled between 4 and 9 seconds.

(e) Distance travelled between 9 and 11 seconds.

(f) Average speed for the whole journey.

A D

C B

5

Scalars and Vectors 1. Divide the following quantities into two lists, one scalars and the other vectors.

mass; speed; area; distance; velocity; displacement; time; acceleration 2. What is your displacement if you fly 50km NE from Dalcross, then 100km NW? 3. Find your displacement if you walk 100m east, then 30m south west, and finally 80m north. 4. A yacht sails due west for 6km, then due north for 8km. It takes 3 hours.

(a) What distance has it travelled?

(b) What is its final displacement?

(c) What is its average speed?

(d) What is its average velocity? 5. A mine locomotive travels 1 km from the top of a mineshaft to the coal tip and back again. The tip is due

east of the mine. What is the locomotive’s final displacement? If the journey takes 10 minutes in each direction, calculate its average speed and its average velocity in ms-1.

6. A cyclist rides 6km NW, 6km S, then turns west and cycles a further 10km. The journey takes her a total

of 1.4 hours.

(a) What distance has she travelled?

(b) What is her final displacement?

(c) What is her average speed?

(d) What is her average velocity? 7. A passenger walks 20m north across the deck of ship. During this time the ship moves 60m east. Find

the passenger's final displacement relative to the earth. 8. An aircraft takes off from Dalcross and flies along compulsory 'air corridors' to its destination. The 'legs'

of its journey are as follows.

180 for 100km; 125 for 88 km; 055 for 65 km; 164 for 175 km

Find the aircraft's final displacement at the end of the journey. 9. A trawler sets out from Aberdeen and steams 45 km east, then 16 km on a heading of 200o. The skipper

then decides to give up fishing and head for home but has only gone 5 km when the engine breaks down. A tug sets out to rescue the trawler. In what direction should the tug proceed and how far will it have to travel before reaching the trawler.

In practice the direction and distance may be different. Why could this be so?

10. In an orienteering competition, a competitor at point X decides to

go first to point Z then point Y. The location of these points is shown in the diagram. (The diagram is not to scale.) (a) What is the displacement form Z to Y?

(b) What total distance does the orienteer travel?

(c) If she runs at a steady speed of 5ms-1, how long did it take her?

(d) What is her velocity from Z to Y? 11. A model plane is flying due north with a velocity of 24ms-1 when

it is subjected to a gust of wind blowing from west to east at 10ms-1. What is the resultant velocity of the plane?

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12. A motorboat can travel at 3ms-1 through the water. It is going to cross a river that flows at 2ms-1

If the boat sets off directly for the opposite bank, find

(a) its resultant velocity,

(b) its final displacement if the river is 50m wide,

(c) the time taken to reach the far bank. 13. On a day when there was a wind blowing of 50kmh-1 from the south, a helicopter pilot flew at 200kmh-1 due east towards an oil platform located 300km due east of Sumburgh. When the pilot was

due north of the platform, how far had he travelled and how long had this taken him? 14. A skier is skiing forward at 20kmh-1 across the slope of a hillside. She then begins to slip sideways at

a speed of 4kmh-1 as well as continuing forward at her original velocity. What is her resultant velocity? 15. A hovercraft leaves Dover and sets course SE at 12ms-1. A wind is blowing from the NE that carries

the hovercraft sideways at 5ms-1. What velocity should the Captain now set to return to the original velocity?

16. A boat sails a course in the following order: a) Due North for 15km c) Due South for 10km b) Due West for 5km d) South East for 7km Using the information above, draw a scale diagram to find out the displacement of the boat from its starting point. 17. A plane takes off from an airfield and flies at a bearing of 500 for a total distance of 100 nautical

miles. It turns to a bearing of 3400 for a further distance of 60 miles. Turning now to a bearing of 1350, it flies for a distance of 50 miles before turning and flying for home. By using a scale drawing estimate the bearing and the distance of its last leg to the airfield.

18. A boy walks around a rectangle of dimensions 100m by 50m. If he makes one complete circuit in

100s, calculate: a) Total distance travelled c) Displacement b) Average speed d) Average velocity

19. A car travels 50km North and then returns 30km South. The whole journey takes 2 hours. Calculate: a) Total distance travelled c) Displacement b) Average speed d) Average velocity

20. An aircraft has a maximum speed of 1000kmh-1. If it is flying into a head wind of speed100kmh-1, what is the velocity of the aircraft relative to the ground? 21. A model aircraft is flying North with a velocity of 24ms-1. A wind is blowing from West to East at

10ms-1. What is the resultant velocity of the plane?

22. An aircraft pilot wishes to fly North at 800kmh-1. A wind is blowing at 80kmh-1 from West to East. What speed and course must he select in order to fly the desired course?

23. A girl delivers newspapers to three houses X, Y and Z as shown in the diagram, starting at X. The girl walks directly from one house to the next. a) Find the total distance the girl walks. b) Calculate the girl’s final displacement from X. c) If the girl walks at 1ms-1, calculate the time she takes to get from X to Z. d) Calculate her resultant velocity.

24. A train is crossing a bridge at 40kmh-1 north and a boat passing below the bridge at 20kmh-1 west. What is the velocity of the train relative to the boat?

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1. (2000)Which of the following is a scaler quanity?

A Velocity

B Accelaration

C Mass

D Force

E Momentum

Past exam questions: Scalers & Vectors

2. (2001)Which one of the following pairs contains one vector quantity and one scalar quantity?

A Force, kinetic energy.

B Power, speed

C Displacement, acceleration

D Work, potential energy

E Momentum, velocity

3. (2003) Which of the following are both vectors? A Speed and weight

B Kinetic energy and potential energy

C Mass and momentum

D Weight and momentum

E Force and speed

4. (1997) Which of the following groups contains two vector quantities and one scalar quantity?

A Time, distance and force

B Acceleration, mass and momentum

C Velocity, force and momentum

D Displacement, velocity and acceleration

E Speed, distance and momentum

5. (1998) Consider the following three statements made by pupils about scalars and vectors.

I Scalars have direction only. II Vectors have both size and direction. Ill Speed is a scalar and velocity is a vector. Which statement(s) is/are true?

A I only

B I and II only

C I and III only

D II and III only

E I, II and III

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Adding Force Vectors 1. Find the resultants of the following pairs of forces by scale drawing.

2.

Find the resultant force of this system. 3. The diagram shows the more

important forces acting on a jet fighter in flight.

(a) What is the net horizontal force?

(b) What is the net vertical force

(c) What is the net overall force? 4. The forces acting on a 6000 kg helicopter are its weight, 64,000 N lift, forward engine thrust of 5 kN to

the right and a horizontal friction of -2 kN acting to the left.

(a) Draw a diagram with all four forces shown.

(b) Draw a second diagram showing only the resultant horizontal and vertical forces.

(c) Draw an accurate scale diagram to find the single resultant force vector acting on the helicopter.

(d) Calculate the acceleration of the helicopter.

a b c d

e f g h

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5. Two husky dogs are pulling a sled with forces of 25N and 35N. Their ropes make angles of 30o and 20o with the direction SF in which the sled is facing. What is the resultant force on the sled?

6. Two electric locomotives, A and B are towing a tanker in the Panama Canal. Each locomotive exerts

a pull of 100kN and the cables from the tanker to each locomotive makes an angle of 60o at the tankers bows. What is the resultant force on the tanker?

7. A monkey, weighing 50N, hangs by its tail and one arm. If the angle between its arm and its tail is

70o, and the angle between its arm and the vertical is 25o, find the force exerted by its tail. 8. An ice puck of mass 0.5 kg is pulled by two elastic threads each exerting a horizontal force of 0.1 N.

Find the acceleration of the puck when the angle between the threads is (a) 0o (b)30o (c) 60o (d) 90o (e) 120o.

9. A crate of mass 25 kg is supported symmetrically by two ropes, each of breaking strain 1000 N. Find

the maximum angle between the ropes before the ropes break? 10. A barge is dragged along a canal as shown.

a) What is the component of the force parallel to the canal?

b) If the barge travels at a constant speed, what is the size of the drag force in the water?

11. A toy train of mass 0.2kg is given a push of 10 N at an angle of 30o to the rails. Calculate the

component of force along the rails, and hence find the acceleration of the train.

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Components 1. Find the horizontal and vertical components of the following vectors.

(a) (b) (c) 2. A garden roller is pulled with a force of 200 N at 50o to the horizontal. Calculate its horizontal and verti-

cal components. 3. A ball is projected from point O with a velocity of 17 ms-1 as shown. Calculate the initial horizontal and vertical components of the ball. 4. A block of mass 5 kg rests on an inclined plane, which makes an angle of 40o to the horizontal. Calculate

the components of its weight, perpendicular and parallel to the plane. If the slope is frictionless, what will be the acceleration of the block down the slope? 5. A metal ball is launched at an angle of 30o and hits a horizontal surface at the same height as the top of the

launcher. The point of impact is 34.6 m away and the ball takes 2 seconds to travel this distance.

(a) Calculate the horizontal velocity of the ball. (b) Calculate the velocity of the ball at the moment of projection.

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6. A 2 kg mass is hanging by a string from the roof. A horizontal force is applied to hold the string in the position shown in the diagram. The tension (force) in the string is 22.6 N. Calculate the horizontal force exerted by the spring balance.

7. A skier is being towed at constant

speed up a ski slope by a tow cable as shown in the diagram.

If the force T exerted by the tow cable

on the skier is 600 N, find the work done by this force in moving the skier 20 m along the slope.

8. a) What is the sum of the forces shown below? (Magnitude only). b) Three forces A, B and C act as shown at a point on an object. Find the resultant force acting on the object.

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1. (2000) A woman walks 12km due North. She then turns round immediately and walks 4km due South. The total journey takes 4 hours. Which row in the following table gives the correct values for her average velocity and average speed?

Average velocity

Average speed

4 kmh -1 due N

4kmh -1

4 km h -1 due N

2 kmh -1

3 kmh -1due N

4 kmh -1

2 kmh -1due N

4 kmh -11

2 kmh -1d u e N

3 kmh -1

A

B

C

D

E

3. (2001)The diagram below shows the resultant of two vectors.

Which of the diagrams below shows the vectors which could produce the above resultant?

2. (1996) A car travels from X to Y and then it travels from Y to Z, as shown in the following diagram

X to Y takes a time of one hour. Y to Z also takes one hour. Which of the following is a correct list of the magnitudes of the final dis-placement, average speed and average velocity for the complete journey?

A

B

C

D

E

Displacement (km)

Average speed (kmh -11)

Average velocity (kmh -1)

50 35 35

70 35 25

50 35 25

70 70 50

50 70 25

Past exam questions: Vector analysis

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4. (1998) Two boys are pulling a car of mass 800 kg along a level surface with a pair of ropes attached horizontally as shown below.

When the pull on each rope is 400 N in the directions indicated, the acceleration of the car is 0.1ms-1. What is the size of the frictional force acting on the car in the above situation? A 194N

B 434 N

C 533N

D 672 N

E 832N

5.(1999) A long-distance athlete runs from point P to point Q and then jogs to point R. She takes 20 minutes to run from P to Q and then a further 40 minutes to jog from Q to R.

Which row in the following table correctly gives her average speed and her average ve-locity for the whole journey from P to R?

A

B

C

D

E

Average speed Average velocity 7.0kmh-1 5.0kmh-1 on a bearing of 143°

7.0kmh-1 7.0 km h-1 on a bearing of 1 27°

7.0kmh-1 5.0kmh-1 on a bearing of 127°

5.0kmh-1 7.0km h-1 on a bearing of 1 27°

5.0kmh-1 5.0kmh-1 on a bearing of 143°

Past exam questions: Vector analysis

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6. (1997) Two ropes are used to pull a boat at constant speed along a canal. Each rope exerts a force of 150N at 20° to the direction of travel of the boat as shown. (a) Calculate the magnitude of the resultant force exerted by the ropes. (b) What is the magnitude of the frictional force acting on the boat? 3

7. (1998) A spectator at A walks to C, the opposite corner of a playing field, by walking from A to B and then from B to C as shown in the diagram below. The distance from A to B is 50m. The distance from B to C is 150m

By scale drawing or otherwise, find the resultant displacement. Magnitude and direction are required. 3

8. (1997) During a flight an aircraft is travelling with a velocity of 36 ms-1 due north (000) .A wind with speed of 36 ms-1 starts to blow towards the direction 40° west of north (320) Find the magnitude and direction of the resultant velocity of the aircraft. 3

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9. (2001) (a) A box of mass 18kg is at rest on a horizontal frictionless surface. A force of 4.0 N is applied to the box at an angle of 26 ° to the horizontal (i) Show that the horizontal component of this force is 3.6 N. (ii) Calculate the acceleration of the box along the horizontal surface. (iii) Calculate the horizontal distance travelled by the box in a time of 7.0s. (b) The box is replaced at rest at its starting position. The force of 4.0 N is now applied to the box at an angle of less than 26 ° to the horizontal.

The force is applied for a time of 7.0 s as before. How does the distance travelled by the box compare with your answer to part (a)(iii)? You must justify your answer. 2

5

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Graphs of Motion 1. The following two graphs show how the velocity of two cars varies with time. Both cars start and stop at the

same time and travel on a straight road.

a) Describe in general terms the motion of car A over sections OP, PQ and QR.

b) Repeat for car B.

c) Which car covered the greater distance? Justify your choice.

d) Calculate the acceleration of car A over OP.

e) Calculate the deceleration of car B over QR.

f) The average speed for car A’s entire journey is 12ms-1. Calculate the travelled during QR. 2. The following velocity-time graphs represent the motion of an object moving in a straight line. Sketch the

corresponding acceleration-time graphs. 3.

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.3 Three velocity-time graphs are shown below

(a) Which graph could represent the motion of a ball dropped onto a hard surface and bouncing back to its original height 0 25 seconds later?

(b) Sketch the corresponding acceleration-time graphs. 4. Three velocity-time graphs are shown below.

(a) Which graph could represent the motion of a ball thrown vertically upwards?

(b) How long did the ball take to reach its highest point?

(c) Sketch the corresponding acceleration-time graphs.

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5. The following acceleration-time graphs represent the motion of objects travelling in a straight line starting from rest. Sketch the corresponding velocity-time graphs.

6. The following velocity-time graphs represent the motion of objects travelling in a straight line

7. The velocity-time graph opposite represents the motion of a girl running for a bus. She runs from a standstill at O and jumps on the bus at Q. Find

(a) the steady speed she at which she runs

(b) the distance she runs

(c) the acceleration of the bus.

(d) Give one possible reason why the ball did not bounce back to the level of the windows.

For each graph

(a) calculate the acceleration

(b) calculate the distance gone

(c) compare the distance gone with the

displacement

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8. A ball is dropped from a window of a tower block onto the concrete yard below. The velocity-time graph of its motion is shown below

(a) How long does it take the ball to reach the ground?

(b) How high is the window above ground level?

(c) To what height did the ball bounce?

(d) Give one possible reason why the ball did not bounce back to the level of the windows.

9. The following information describes the motion of an elevator in a New York skyscraper as it travels from

the ground floor to the 12th floor.

Uniform acceleration from rest to 5ms-1 in 6 seconds.

Uniform speed for 4 seconds.

Uniform deceleration to rest in 6 seconds.

(a) Draw a velocity-time graph for the 16 second journey.

(b) Draw an acceleration-time graph for the journey.

(c) Calculate the height of the 12th floor from ground level. 10. From the graph calculate

(a) the acceleration between A and B

(b) the acceleration between C and D

(c) the total distance travelled

(d) the average speed for the whole journey.

11. The following is a graph of the velocity of a ball. The graph has been ‘ idealised’ in that no friction losses have been taken into account.

a) Give a full description of the motion of this ball. Use a sketch of the graph, suitably labelled, to indicate what is happening at all the significant events and intervals on the graph.

b) Using graph paper, draw the corresponding graph of acceleration against time for the motion of the ball.

A D

C B

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12. a).A ball is thrown upwards and allowed to drop onto a hard floor and bounce repeatedly. Assuming that no energy is lost during bounces, draw a velocity-time graph of the motion of the ball over a number of bounces starting from when it was dropped. b). Repeat for a real situation where energy is lost at each contact with the ground.

13. Use the information given in the table below to calculate the acceleration of the trolley.

14. The velocity-time graph of a moving body is shown below. Find from the graph: a) The maximum acceleration b) The total distance covered.

15. A car travels along a straight road. Its speed-time graph is shown below.

a) Which stage of the journey took the longest time? b) During which stage of the journey is - i). The speed greatest? ii). The acceleration greatest? c) During which stage of the journey does the car travel the greatest distance? d) Calculate the acceleration of the car during stage 1.

Length of card = 5cm time 2 = 0.05s

Time 1 = 0.01s

time 3 = 2.50s

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16. A car accelerates from rest to 10 ms-1 in a time of 5s, travels at a constant speed for 12s, then brakes suddenly and comes to rest in a further 2s.

a) Draw the car’s speed-time graph.

b) State any assumptions made in drawing the graph.

c) What was the car’s speed 3s after the start?

d) Draw an acceleration-time graph for the car.

e) Explain why, in practice, graphs of the type you have drawn would not be obtained.

f) If the car had been full of passengers, and the driver had operated the controls in exactly the same

way, redraw the graphs of a) and d) to show how the motion would be modified.

17. A space probe is rising vertically from the surface of a planet when its engines suddenly cut off. The

graph below shows how the velocity of the probe varies with time from the instant of lift off.

a) On a sketch of this graph label the significant events occurring at points P, Q, R, S and T. Label

also the line segments PQ, QR, RS and ST as to what is happening to the space probe during each of these intervals.

b) On a piece of squared paper draw an acceleration-time graph of the motion. c) What is the acceleration of a free falling body on this particular planet? 18. You are running at your maximum speed of 6ms-1 to catch a bus, which is standing at the bus stop. The

bus moves off with an acceleration of 1ms-2 when you are 20m from it. Find graphically if you catch the bus.

22

1. (2000) The following velocity-time graph describes the motion of a ball, dropped from rest and bouncing several times

Which of the following statements is/are true?

I The ball hits the ground at P. II The ball is moving upwards between Q andR.

III The ball is moving upwards between R and S.

A I only

B II only

C III only

D I and II only

E I and III only

3. (2002) The following graph shows how the displacement of an object varies with time.

From O to P

From P to Q

constant acceleration

constant velocity

zero velocity

constant deceleration

constant velocity

zero velocity

zero velocity

constant velocity

constant velocity

constant deceleration

A

B

C

D

E

Which row of the table below best describes the motion of this object?

2. (1998) The velocity– time graph for an object traveling along a straight line is shown below.

The displacement of the object during the first 12 seconds is

A 18m

B 24m

C 30m

D 36m

E 54m.

Past exam questions: Graphs of motion

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4. (2002) Which of the following velocity-time graphs best describes a ball being thrown vertically into the air and returning to the thrower's hand?

5. (2003) A vehicle is traveling in a straight line. Graphs of velocity and acceleration are shown below. Which pair of graphs could represent the motion of the vehicle?

24

6. (1996) A lift in a hotel makes a return journey from the ground floor to the top floor and then back again. The corresponding velocity-time graph is shown below.

Which of the following shows the acceleration-time graph for the same journey?

7. (1997) The diagram below is the velocity-time graph for a model train moving along a straight track.

Which of the following could represent the displacement-time graph for the same motion?

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8. (1998) The following is a speed-time graph of the beginning of a cyclist's journey along a straight track.

Which of the following could be the corresponding acceleration-time graph for the same period?

9. (1998) The velocity-time graph for an object travelling in a straight line is shown below.

Which one of the following is the correspondding acceleration-time graph?

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10. (1999) A bungee jumper is attached to a high bridge by a thick elastic rope as shown.

The graph shows how the velocity of the bungee juniper varies with time during the first 6 seconds of a jump.

The mass of the bungee jumper is 55 kg. (a) Using the information on the graph, state the time at which the bungee rope is at its maximum

length. Justify your answer. (b) Calculate the average unbalanced force, in newtons, acting on the bungee jumper between the points A and B on the graph. (c) Explain, in terms of the force of the rope on the bungee jumper, why an elastic rope is used rather than a rope that cannot stretch very much.

2

2

2

27

11. (2002) A basketball is held below a motion sensor. The basketball is released from rest and falls onto a wooden block. The motion sensor is connected to a computer so that graphs of the motion of the basketball can be displayed.

A displacement-time graph for the motion of the basketball from the instant of its release is shown.

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(a) (i) What is the distance between the motion sensor and the top of the basketball when it is released?

(ii) How far does the basketball fall before it hits the wooden block? (iii) Show, by calculation, that the acceleration of the basketball as it falls is 8.9ms-2

(b) The basketball is now dropped several times from the same height. The following values are obtained for the acceleration of the basketball.

8.9 ms-2 9.1 ms-2 8.4 ms-2 8.5ms-2 9.0 ms-2 Calculate:

(i) the mean of these values; (ii) the approximate random uncertainty in the mean.

(c) The wooden block is replaced by a block of sponge of the same dimensions. The experiment is repeated and a new graph obtained.

Describe and explain any two differences between this graph and the original graph.

3 3 2

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Equations of Motion 1. A car passes you at10ms-1 and accelerates uniformly for 10 seconds at 2.0ms-2. What is its speed after

10 seconds? 2. How high is a cliff if a stone takes 1.5 sec to fall to the beach? 3. If the speed of a spacecraft is reduced uniformly from 2000ms-1 to 200ms-1 in 30s, find the distance

travelled in that time. 4. How fast is a free fall parachutist going after falling 0.l0km? 5. A bicycle travelling at 15ms-1 stops in 3.0sec. What is its acceleration? 6. Part of an exploding star starts from rest and travels 4.0km in 4.0s. What is its acceleration? 7. A car is braked from 30ms-1 to 20ms-1 in 100m. Find the acceleration. 8. The height of the main towers of the Forth Bridge is 160m. How long will a spanner, dropped from the

top of one of the towers, take to reach the water? 9. A spacecraft to Mars is travelling at 2000ms-1 when the rocket is fired. The motor produces a constant

acceleration of 10ms-2 and bums for 300 seconds.

(a) Find the final speed of the spacecraft.

(b) How far did it travel during this time? 10. A paint tin, dropped from the roof of a skyscraper, takes 9.0 s to reach the ground.

(a) Calculate its velocity as it hits the ground.

(b) What is the height of the building? 11. Giovanni Graviti drops a pebble from the top of the Leaning Tower of Pisa and it takes 3.2s to reach the

ground below.

(a) Calculate the pebble’s velocity as it hits the ground.

(b) How high is the Leaning Tower of Pisa? 12. After falling for 10 s, a stone had a downward velocity of 120ms-1. What velocity must it have had at the

start of the 10 seconds? 13. A ball is thrown upwards with a velocity of 20ms-1. After what time will it reach a height of 15m?

Explain why there are two correct answers. 14. A stone is thrown vertically down a well shaft at 15ms-1.

(a) How fast will it be travelling when it hits the water 60m below?

(b) How long does it take the stone to reach the water? 15. An arrow is fired vertically upwards with a velocity of 80 ms-1.

(a) What is the arrow’s velocity at its maximum height?

(b) How long does it take to reach its maximum height?

(c) What is its maximum height

(d) How long does it take to fall from the maximum height back to earth?

30

16. At the instant the traffic lights turn green a police car accelerates from rest at 6 ms-2. At the same instant a truck travelling at a constant speed of 30 ms-1 overtakes the police car.

(a) At what distance from the traffic lights will the police car catch up with the truck? (b) How fast will the police car be travelling at that instant? 17. A stone thrown vertically upwards takes 4.0 s to return to the ground.

(a) What is its displacement when it has returned to its starting position

(b) What was the stone’s initial velocity

(c) What was the stone’s velocity at the highest point?

(d) What was the greatest height reached by the stone?

(e) What was the stone’s average velocity during its motion? 18. A helicopter is rising vertically at 10 ms-1 when a wheel drops off and reaches the ground 8.0 s later. At

what height was the helicopter flying when the wheel fell off? 19. A helicopter that is ascending at a steady speed of 10ms-1 releases a parcel that then takes 5.0 s to reach the

ground.

(a) Find the speed of the parcel when it hits the ground.

(b) What was the height of the helicopter when the parcel was released?

(c) What was the maximum height of the parcel above the ground?

(d) Where is the helicopter when the parcel hits the ground? 20. Bob Slade pushes himself off at a speed of 2.0ms-1 from the top of a downhill run on his home-made ski

jump. This straight run of 40m increases Bob’s speed to 22.0ms-2.

(a) What is his acceleration on this downhill run?

(b) What is his speed 30m from the start?

(c) How much time does Bob take to complete his downhill run? 21. A ball bearing is dropped vertically and it enters a cardboard tube that is 40cm long. The ball is out of

view for 0.20 s.

(a) What is the speed of the ball bearing as it enters the tube?

(b) What is its speed as it emerges from the tube? 22. A ball is kicked vertically upwards with a

velocity of +20ms-1 from the edge of a cliff. It lands with a velocity of -50ms-1 at the bottom of the cliff.

(a) What is the velocity of the ball at its highest point?

(b) What is the total time the ball is in the air?

(c) Draw a velocity-time graph for the total motion.

(d) How high above the cliff did the ball reach?

31

1. (2001)A helicopter is descending vertically at a constant speed of 3.0ms- 1 . A sandbag is released from the helicopter. The sandbag hits the ground 5.0 s later.

What was the height of the helicopter above the ground at the time the sandbag was released?

A 15.0m

B 49.0 m

C 107.5m

D 122.5m

E 137.5m

Assuming that the acceleration due to gravity is 9-8 ms -2 , the acceleration of the box is

A 2.2ms-2

B 7.6ms-2

C 9.8ms-2

D 12.0ms-2

E 19.6ms-2.

2. (2002) A force of 180N is applied vertically upwards to a box of mass 15 kg.

4. (1996)An object attached to a parachute falls from a helicopter which is hovering at a height of 120m above point X. The object falls with a constant vertical component of velocity of value 12ms-1 . A steady side-wind gives the object a constant horizontal component of velocity of value 5 m s - 1

How far from point X does the object hit the ground? A 24m

B 50m

C 60m

D 120m

E 150m

3. (1997) A train decelerates uniformly from 12.0ms-1 to 5.0 ms-1 while travelling a distance of 119.0 m along a straight track. The deceleration of the train is A 0.5 ms-2

B 0.7 ms-2

C 1.2 ms-2

D 7.0 ms-2

E 14.0 ms-2

5. (1997) A ball is projected vertically upwards with an initial speed of 40ms-1 . The acceleration due to gravity can be taken to be 10ms-2 . What total time will the ball take to rise to its highest point and then return to its starting point?

A 2s

B 4s

C 6s

D 8s

E 16s

Past exam questions: Equations of Motion

32

6. (1998) In the equation s = ut + ½at2 for an object moving in a straight line with a uniform accel-eration "a", the term "ut" represents A the initial velocity of the object B the initial acceleration of the object

C the velocity of the object after t seconds

D the acceleration of the object after t seconds

E the displacement of the object after t seconds

if the acceleration is zero

33

7.. (1999) A ball is rolled up a slope so that it is travelling at 14 ms-1 as it leaves the end of the slope. (a) The slope is set so that the angle to the horizontal, θ, is 30 °Calculate the vertical component of the velocity of the ball as it leaves the slope. (b) The slope is now tilted so that the angle to the horizontal, θ, is increased. The ball is rolled so that it still leaves the end of the slope at 14 ms-1 Describe and explain what happens to the maximum height reached by the ball. 3

8. (1996) The manufacturers of tennis balls require that the balls meet a given standard. When dropped from a certain height onto a test surface, the balls must rebound to within a limited range of heights. The ideal ball is one which, when dropped from rest from a height of 3.15m, rebounds to a height of 1.75m as shown below. (a) Assuming air resistance is negligible, calculate

(i) the speed of an ideal ball just before contact with the ground

(ii) the speed of this ball just after contact with the ground. 3

(b) When a ball is tested six times, the rebound heights are measured to be

1-71 m, l-78m, l-72m, l-76m, l-73m, l-74m.

Calculate

(i) the mean value of the height of the bounce

(ii) the random error in this value. 3

34

9. (1997) An object starts from rest and moves with constant acceleration a. After a time t, the velocity v

and displacement are given by

v = at and s = ½ at2 respectively.

Use these relationships, to show that

v2= 2as. 2

35

10. (1999) (a) A sports car is being tested along a straight track. (i) In the first test, the car starts from rest and has a constant acceleration of 4.0 ms-1 in a straight line for 7.0 seconds. Calculate the distance the car travels in the 7.0 seconds. (ii) In a second test, the car again starts from rest and accelerates at 4.0 ms-1 over twice the distance covered in the first test. What is the increase in the final speed of the car at the end of the second test compared with the final speed at the end of the first test? (iii) In a third test, the car reaches a speed of 40 ms-1. It then decelerates at 2.5 ms-2 until it comes to rest. Calculate the distance travelled by the car while it decelerates to rest. (b) A student measures the acceleration of a trolley as it moves freely down a sloping track.

The trolley has a card mounted on it. As it moves down the track the card cuts off the light at each of the light gates in turn. Both the light gates are connected to the computer which is used for timing. The student uses a stopclock to measure the time it takes the trolley to move from the first light gate to the second light gate. (i) List all the measurements that have to be made by the student and the computer to allow the acceleration of the trolley to be calculated. (ii) Explain fully how each of these measurements is used in calculating the acceleration of the trolley as it moves down the slope.

7

3

36

Projectiles 1. A projectile is fired horizontally from the edge of a cliff at 12ms-1 and hits the sea 60m away. Find

(a) the time of flight

(b) the height of the cliff. 2. A pebble is thrown horizontally from the top of a 30m high cliff. If it hits the sea 50m from the base of the

cliff find

(a) its initial velocity

(b) the velocity with which it hits the sea. 3. After a shipwreck there are survivors swimming in the sea. As the pilot of a rescue plane you want to drop

a liferaft right beside them. If you are flying at a speed of 120ms-1 and at a height of 25m above the sea, how far away from them should you be when you drop the liferaft?

4. An athlete throws a javelin with an initial velocity of 24ms-1 at an angle of 30o to the horizontal.

(a) What is the maximum height reached by the javelin during its flight?

(b) How far does the javelin travel horizontally? 5. In a game a girl stands on a platform and throws a large plastic dart at a target marked on the ground. The

centre of the target is 5m away from the base of the platform. The platform is 1m high. The dart leaves the girl's hand with a velocity of 6.25ms-1 at an angle of 53o above the horizontal. The dart

is in flight for 1.5 seconds. Calculate how many points the girl scores.

Scoring Distance fromTarget Centre Points within 0.5m 10 0.5 to 1.0m 5 1.0 to 1.5m 3 1.5 to 2.0m 1

37

6. A projectile is fired with a velocity v at an angle a to the horizontal. It returns to the ground at position R. The horizontal and vertical components of its velocity are shown in graphs I and II respectively.

Graph I Graph II

(a) How far from A is the projectile when it hits the ground at R?

(b) There is a disused building 15m high, midway between A and R. What is the distance between the top of this building and the projectile as it passes directly over the building?

(c) Calculate the initial velocity of the projectile. 7. A ski-jumper involved in the Olympic trials left the ramp with a horizontal velocity of 25ms-1 and

managed to 'jump' a vertical displacement of 30m as shown in the diagram.

(a) Calculate the time the skier was in the air.

(b) Calculate the horizontal distance travelled by the skier.

(c) Calculate the velocity of the skier on landing.

38

1. An aeroplane is flying at 160ms-1 in level flight 80m above the ground. It releases a package at a horizontal distance X from the target T

A 40m

B 160m

C 320m

D 640m

E 2560m.

The effect of air resistance can be neglected and the acceleration due to gravity can be taken as 10ms-1. The package will score a direct hit on the target T if X is

2. (1998) A stone is thrown horizontally with a speed of 12ms-1 over the edge of a vertical cliff. It hits the sea at a horizontal distance of 60m out from the base of the cliff.

Assuming that air resistance is negible and that acceleration due to gravity is 10 ms-2 , the height from which the stone was projected above the level of the sea is A 5m

B 25m

C 50m

D 125m

E 250m.

3. (1998)A motorcycle stunt involves crossing a ravine from P to Q. The motorcycle is travelling horizontally when it leaves point P. Neglecting air resistance and taking the acceleration due to gravity to be 10ms-2, the time taken to cross the ravine from P to Q is A 0.125s B 0.25s C 0.5s D 1.0s E 4.0s.

Past exam questions: Projectiles

39

4. (1996) An archer fires an arrow at a target which is 30 m away.

The arrow is fired horizontally from a height of l.5m and leaves the bow with a velocity of 100ms-1. The bottom of the target is 0.9 m above the ground. Show by calculation that the arrow hits the target. Use g = 9.8ms-2 . 3

5. (1997) The fairway on a golf course is in two horizontal parts separated by a steep bank as shown below

A golf ball at point O is given an initial velocity of 41.7ms-1 at 36° to the horizontal. The ball reaches a maximum vertical height at point P above the upper fairway. Point P is 19.6m above the upper fairway as shown. The ball hits the ground at point Q.

The effect of air friction on the ball may be neglected.

(a) Calculate:

(i) the horizontal component of the initial velocity of the ball;

(ii) the vertical component of the initial velocity of the ball. 2

(b) Show that the time taken for the ball to travel from point O to point Q is 4.5 s. 3

(c) Calculate the horizontal distance travelled by the ball. 2

40

6. (2000) At a funfair a prize is awarded if a coin is tossed into a small dish. The dish is mounted on a shelf above the ground as shown.

A contestant projects the coin with a speed of 7.0 ms-1 at an angle of 60 ° to the horizontal. When the coin leaves his hand, the horizontal distance between the coin and the dish is 2.8m. The coin lands in the dish. The effect of air friction on the coin may be neglected. (a) Calculate: (i) the horizontal component of the initial velocity of the coin; (ii) the vertical component of the initial velocity of the coin. (b) Show that the time taken for the coin to reach the dish is 0.8 s. (c) What is the height, h, of the shelf above the point where the coin leaves the contestant's hand? (d) How does the value of the kinetic energy of the coin when it enters the dish compare with the

kinetic energy of the coin just as it leaves the contestant's hand? Justify your answer.

2

1

2

2

41

7. (2003) A golfer on an elevated tee hits a golf ball with an initial velocity of 35.0ms-1 at an angle of 40° to the horizontal. The ball travels through the air and hits the ground at point R. Point R is 12m below the height of the tee, as shown.

The effects of air resistance can be ignored. (a) Calculate: (i) the horizontal component of the initial velocity of the ball; (ii) the vertical component of the initial velocity of the ball; (iii) the time taken for the ball to reach its maximum height at point P. (b) From its maximum height at point P, the ball falls to point Q, which is at the same height as the tee. It then takes a further 0.48s to travel from Q until it hits the ground at R. Calculate the total horizontal distance d travelled by the ball.

4

3

42

Revision of Force, Work and Energy 1. What is the weight of a car of mass 900 kg? 2. A girl’s mass is 70 kg. What is her weight? 3. A boy weighs 650 N. What is his mass? 4. What unbalanced force produces an acceleration of 15 ms-2 on an athlete of mass 55 kg? 5. What resultant force produces an acceleration of 2.0 ms-2 in a car of mass 800 kg? 6. An empty van accelerates along a road at 2ms-2. Why will its acceleration change when it is fully

loaded? 7. Forces are applied to a block as shown. The

block has a mass of 2kg.

(a) Find the resultant force acting on the block

(b) What will be the acceleration of the block?

8. A pupil pulls a desk 4m across a floor, exerting a force of 20N and taking 5 seconds. What is the work

done by the pupil, and what is their power output? 9. A dog pulling a sled exerts 600J of energy in 15 seconds when pulling with a force of 50N. How far did

the dog pull the sled and what power did the dog exert? 10. An electric motor is rated at 1kW and gives out 2400J when lifting a mass weighing 600N. How high

was the mass lifted and how long did it take? 11. A 5kg mass is lifted 2m onto a platform

(a) How much work was done in lifting the mass?

(b) What is the potential energy gained by the mass?

(c) If this had occurred on the moon where the gravitational attraction is 1.6Nkg-1 what would be the potential energy gained?

(d) If the mass was knocked off the platform on the moon, what would be its speed just before it hit the moon's surface.

12. A car of mass 800kg is travelling at 25ms-1 when it reaches a the bottom of a hill. The driver switches off

the engine and freewheels up the hill until the car stops. What vertical height does the car rise? 13. A locomotive of mass 45 tonnes is travelling at 40ms-1 when the driver applies the brakes. The total mass

of the brake pads is 6kg and the material of which they are composed has a specific heat capacity of 680Jkg-1 oC-1. What is the rise in temperature of the brake pads?

43

14. A pendulum is pulled to the side as shown in the diagram and released.

(a) What is its potential energy before release?

(b) What is its maximum potential kinetic energy?

(c) Find its maximum speed.

(d) What assumption have you made in calculating the answer to (b)?

15. An object is placed at the top of a slope as shown.

It is released and rolls down the slope reaching the bottom of the slope with a speed of 2.5ms-1.

(a) Calculate its potential energy at the top of the slope

(b) Find its kinetic energy at the foot of the slope

(c) How much work is done against friction?

(d) How much energy is lost in the form of heat?

(e) Calculate the average force of friction. 16. A body of mass 5kg enters the earth’s atmosphere moving at 104 ms-1. After 20 seconds its speed is

reduced to 100 ms-1. Find

(a) the average retarding force on the body,

(b) the heat generated.

(c) Draw graphs showing how (i) the acceleration varies with time, (ii) the force varies with time, (iii) the velocity varies with time. 17. A trolley of mass 10kg is accelerated for 2s from rest by an unbalanced force of 5N then moves at

constant speed for the next 3s and gradually slows down to rest in 6 s.

(a) Draw graphs showing the variation of (i) force applied against time, (ii) acceleration against time, (iii) velocity against time.

(b) Calculate the distance covered in the 11s.

(c) What is the average speed of the trolley?

44

1. (2003) A car of mass 1000kg is travelling at a speed of 40ms-1 along a straight road. The brakes are applied and the car decelerates to 10ms-1 . How much kinetic energy is lost by the car? A 15 kJ

B 50kJ

C 450kJ

D 750 kJ

E 800kJ

Past exam questions: Energy

45

Force and Acceleration

1. A balloon is tethered to the ground as shown. (a) Draw a diagram showing the forces acting on the balloon.

(b) When the rope holding the balloon to the ground is released, the balloon rises. Explain in terms of the forces applying to the balloon why this happens.

2. A rocket of mass 1500 kg has 4 motors each producing a constant thrust of 4000N.

The motors are fed fuel from tanks containing liquid hydrogen and oxygen.

(a) Draw a diagram to show the forces acting on the rocket;

(a) Calculate the total thrust produced by the motors.

(b) What is the weight of the rocket?

(c) Find the initial acceleration of the rocket.

(d) As time passes the acceleration of the rocket increases. Suggest a reason for this. 3. A car of mass 1000kg accelerates steadily from rest to 30ms-1 in 15 seconds.

(a) What is its acceleration?

(b) What resultant force produces this acceleration?

(c) The actual force supplied by the engine will be greater. Explain why. 4. A trolley of mass 3.0 kg, resting on a rough surface, was pulled by a force of 9.0 N. After10 seconds its

speed was 20 ms-1. Find

(a) its average acceleration,

(b) the average frictional force exerted on the trolley. 5. The graph shows how the downward speed of a lift varies with time.

(a) Draw an acceleration time graph

(b) A 4kg mass is suspended from a spring balance inside the lift. Determine the lift reading on the balance at each stage of the motion.

rope

46

6. Two blocks of wood, which are in contact with each other, are accelerated along a bench top at 6ms-2 by a force.

(a) Find the total force applied

(b) Find the force applied to the 2kg block 7. A sky diver jumps out of a plane. Sketch the vertical forces acting on him when he has

(i) just jumped out of the plane,

(ii) opened his parachute. 8. Two frictionless pucks are tied together by a thread and pulled by a spring balance reading 7.5 N. If the

pucks have masses of 1 kg and 1.5kg respectively, calculate

(a) the tension in the string joining them.

(b) the unbalanced force acting on each puck. 9. Three trolleys are pulled down a friction-compensated slope by a force of 1 N.

Find the tensions T1 and T2. 10. A body of mass 2 kg is pulled up a smooth slope inclined at 30o to the horizontal by a force of 15N. Find

(a) the unbalanced force acting on the body parallel to the slope,

(b) the time taken to pull the body from rest 8m up the slope.

11. A car of mass 900kg sits at rest on a 25o slope. The driver releases the hand brake and the car starts to roll

down the hill for 5 seconds. Find

(a) the acceleration down the slope,

(b) the distance travelled,

(c) the speed attained.

(d) If the driver now applies the brakes exerting a frictional force of 1000N, how long does the car take to come to rest?

47

12. Find the apparent weight of the person standing in the lifts shown. The motion of each lift is shown underneath.

13. A 130 kg mass hangs by a cable from the jib of a crane. What is the tension in the cable when the 130kg mass is

(a) at rest,

(b) accelerating upwards at 3ms-2

(c) rising at a steady speed of 5ms-1

(d) accelerating downwards at 4ms-2 ? 14. A block of wood, mass 300g has to be held stationary on a plane inclined at 300 to the horizontal by a force acting parallel to the plane. Calculate the magnitude of this force.

Mass of person 50kg 50kg 60kg

Motion of lift Steady speed Accelerating Accelerating downwards of upwards at downwards at 5 ms-1 2 ms-2 2 ms-1

Mass of person 50kg 50kg

Motion of lift Accelerating Accelerating upwards at downwards at 5 ms-2 3 ms-2

48

1. (2001) A car of mass 900kg pulls a caravan of mass 400kg along a straight, horizontal road with an acceleration of 2.0 ms-1

Assuming that the frictional forces on the caravan are negligible, the tension in the coupling be-tween the car and the caravan is

A 400 N

B 500N

C 800N

D 1800N

E 2600N.

2. (2002) A helium filled balloon of mass 1.5kg floats at a constant height of 100m. The acceleration due to gravity is 9.8ms-2.

The upthrust on the balloon is

A 0N

B 1.5N

C 14.7N

D 150N

E 1470 N.

4. (2003) A block of mass 4.0 kg and a block of mass 6.0 kg are linked by a spring balance of negligible mass.

The blocks are placed on a frictionless horizontal surface. A force of 18.0 N is applied to the 6.0 kg block as shown.

What is the reading on the spring balance? A 7.2N

B 9.0 N

C 10.8N

D 18.0N

E 40.0 N

5. (1996) A horizontal force of 20N is applied as shown to two wooden blocks of masses 3 kg and 7 kg. The blocks are in contact with each other on a frictionless horizontal surface

What is the size of the horizontal force acting on the 7kg block? A 20N

B 14N

C 10N

D 8N

E 6N

3. (1999) A crane on an oil-rig is used to raise a sunken buoy from the seabed. The weight of the buoy is 4900 N and the buoyancy force (upthrust) acting on it is 1000N. When the buoy is being raised vertically at a constant speed, a force of 800 N acts on it due to water resistance. What is the size of the force which the vertical cable applies to the buoy?

A 200 N

B 1800N

C 3100N

D 4700N

E 6700N

Past exam questions: Forces

49

6. (1996) An object of mass 1.0kg hangs from a spring balance which is suspended on the inside of a small rocket, as shown below.

What is the reading on the balance when the rocket is accelerating upwards from the earth’s surface at 2.0ms-1 A 0N

B 2.0N

C 7.8N

D 9.8N

E 11.8N

7. (1997)The lift in a department store has a mass of 1100kg.

The lift is descending with a uniform downwards acceleration of 2ms-2. The acceleration due to gravity can be taken as 10ms-2 What is the force applied to the lift by the lift cable? A 1100N

B 2200 N

C 8800 N

D 11000N

E 13200N

8. (1998) A rocket of mass 200kg accelerates vertically upwards from the surface of a planet at 2 ms-2 . The gravitational field strength on the planet is 4Nkg-1. What is the size of the force being supplied by the rocket's engines? A 8OON

B 1200N

C 2000 N

D 2400 N

Weight

Air resistance

Upthrust

100 N

100 N

200 N

100 N

100 N

210N

100 N

100 N

I O N

1 0 N

100 N

120 N

100 N

100 N

100 N

9. (1998) A balloon of mass 10kg accelerates vertically upwards with a constant acceleration of 1ms-2. The air resistance acting on the balloon is 100N. Assuming that the acceleration due to gravity is 10ms , which row in the following table shows the size and direction of the forces acting on the balloon?

A

B

C

D

E

50

10 (1996)A mooring buoy is tethered to the seabed by a rope which is too short. The buoy floats under the water at high tide. The weight of the buoy is 50 N (a) (i) Draw a labelled diagram to show all the forces acting on the buoy in the vertical direction. (ii) The tension in the rope is 1200 N. Calculate the buoyancy force. (b) The rope now snaps and the buoy starts to rise. What is the size of the buoyancy force on the buoy when it is just below the surface of the water?

11 (1997)The diagram shows a weather balloon of mass m tethered by a rope to the ground.

(a) Draw a sketch of the balloon. Mark and name all the forces acting vertically on the balloon. (b) What is the resultant force acting on the balloon? 2

12. (1997) An aircraft of mass of 1000kg has to reach a speed of 33 ms-1 before it takes off from a run-way. The engine of the aircraft provides a constant thrust of 3150N. A constant frictional force of 450 N acts on the aircraft as it moves along the runway.

(i) Calculate the acceleration of the aircraft along the runway. (ii) The aircraft starts from rest. What is the minimum length of runway required for a take-off? 4

2

2

51

2

2

1 2

13. (1998)A student performs an experiment to study the motion of the school lift as it moves upwards.

The student stands on bathroom scales during the lift's journey upwards. The student records the reading on the scales at different parts of the lift's journey as follows.

(a) Show that the mass of the student is 60 kg.

(b) Calculate the initial acceleration of the lift.

(c) Calculate the deceleration of the lift.

(d) During the journey, the lift accelerates for 1.0s, moves at a steady speed for 3.0s and

decelerates for a further 1.0s before coming to rest.

Sketch the acceleration-time graph for this journey.

Part of journey

Reading on scales

At the start (while the lift is accelerating)

678 N

In the middle (while the lift is moving at a steady speed)

588N

At the end (while the lift is decelerating)

498 N

52

The box accelerates at 10ms-2 up the plane. The size of the force of friction opposing the mo-tion of the box is A 50N

B 100 N

C 150N

D 200 N

E 250N.

1. (2002)A box of mass 10kg rests on an inclined plane. The component of the weight of the box acting down the incline is 50N. A force of 500N, parallel to the plane, is applied to the box as shown.

2. (1996) A sledge is dragged at a constant velocity along the snow against a horizontal frictional force F. The rope pulling the sledge is at an angle of θ to the horizontal, as shown

When the sledge is moving horizontally with a constant velocity, the force P pulling the rope is equal to A F B F cos θ C F sin θ D F cos θ E F sin θ

3. (1997) A sledge is pulled a distance of 8m in a straight line along a horizontal surface.

The tension in the rope is 75 N and the angle be-tween the rope and the horizontal surface is 28°. Which row in the following table is correct?

Horizontal

component of tension /N

Vertical com-ponent of tension /N

Work done by rope /]

75 sin 28° 75 sin 62° 600

75 cos 28° 75 sin 28° 530

75 sin 62° 75 sin 28° 600 75 cos 28° 75 sin 62° 600 75 sin 28° 75 cos 28° 35

A

B

C

D

E

Past exam questions: Forces on a slope

53

4. (1996) A child on a sledge slides down a slope which is at an angle of 20o to the horizontal as shown below

The combined weight of the child and the sledge is 400 N. The frictional force acting on the sledge and child at the start of the slide is 20.0 N. (a) (i) Calculate the component of the combined weight of the child and sledge down the slope. (ii) Calculate the initial acceleration of the sledge and child. (b) The child decides to start the slide from further up the slope. Explain whether or not this has any effect on the initial acceleration. (c) During the slide, the sledge does not continue to accelerate but reaches a constant speed. Explain why this happens.

4

2

2

54

5. (1998) A trolley of mass 2.0 kg is catapulted up a slope. The slope is at an angle of 20° to the horizontal as shown in the diagram below. The speed of the trolley when it loses contact with the catapult is 3.0 ms-1

The size of the force of friction acting on the trolley as it moves up the slope is 1.3 N. (a) (i) Calculate the component of the weight of the trolley acting parallel to the slope. (ii) Draw a diagram to show the forces acting on the trolley as it moves up the slope

and is no longer in contact with the catapult. Show only forces or components of forces acting parallel to the slope. Name the

forces. (iii) Show that, as the trolley moves up the slope, it has a deceleration of magnitude 4.0 ms -2. (iv) Calculate the time taken for the trolley to reach its furthest point up the slope (v) Calculate the maximum distance the trolley travels along the slope.

The trolley now moves back down the slope. (b) (i) Draw a diagram to show the forces acting on the trolley as it moves down the slope. Show only forces or components of forces acting parallel to the slope. Name the forces. (ii) The magnitude of the deceleration of the trolley is 4.0 ms-2 as it moves up the slope. Explain why the magnitude of the acceleration is not 4.0 ms-2 when the trolley moves down the slope.

9

2

55

Momentum 1. Find the momentum of a trolley of mass 2 kg travelling at 3 ms-1. 2. A trolley of mass 3 kg and momentum 18 kg ms-1.would travel with what velocity? 3. A car with momentum 1620 kg ms-1.has a mass of 1160 kg. What is the velocity of the car? 4. A cyclist with momentum 620 kg ms-1.travels at a speed of 14 ms-1.. What is the mass of the cyclist? 5. A trolley of mass 3 kg travelling at 4 ms-1.collides with a trolley of mass 1 kg that is at rest. After the

collision the trolleys stick together. With what velocity do the trolleys move off at after the collision. 6. A target of mass 4 kg hangs from a tree by a long string. An arrow of mass 100 g is fired with a velocity

of 100 ms-1.and embeds itself in the target. With what velocity does the arrow and target move after the impact?

7. A bus of mass 4000 kg travelling at 20 ms-1.collides inelastically with a lorry approaching from the

opposite direction at 32 ms-1.. If the lorry has a mass of 2500 kg, with what velocity do the bus and the lorry move off at after the collision?

8. A trolley of mass 2 kg moving at 6 ms-1.strikes another trolley of mass 4 kg that is stationary. After the

collision, the first trolley remains stationary. What is the velocity of the second trolley after the collision? 9. Two trolleys, each of mass 3 kg, collide head on with speeds of 5 and 2 ms-1.. If they stick together after

the collision, what is their combined velocity? 10. A trolley moving at 12 ms-1. hits an identical trolley moving at 4 ms-1.in the same direction. Afterwards

the first trolley has a velocity of 6 ms-1.. What is the speed and direction of the second trolley? 11. Two identical trolleys separate explosively by means of a spring plunger. If one trolley moves to the

right with a velocity of 7 ms-1.what will be the velocity of the other trolley? 12. A satellite splits into two parts, one part being five times the mass of the other part. If the smaller part

moves off with a velocity of 25ms-1.what will be the velocity of the larger part? 13. A plane of mass 18000kg is travelling at 400ms-1.when it fires a projectile forward. The projectile has a

mass of 100kg and travels at a speed of 200ms-1.relative to the plane. What is the speed of the plane after the projectile has been fired?

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14. A boy is playing with a toy snooker table, each ball having a mass of 0.1 kg. He plays the white ball that strikes a red ball that is at rest. The velocity of the white ball was 2 ms-1.and after the collision the white ball remains stationary and the red ball moves off at 2 ms-1..

(a) (i) Show that momentum was conserved in the collision.

(ii) Show that Ek was conserved in the collision.

(iii) What type of collision was it?

(b) The boy loses the blue ball and replaces this with an old rubber ball that has a mass of 0.1 kg also. He now plays a shot as before. The white ball strikes the motionless blue ball at 2.5 ms-1.and after the collision the blue ball moves off at 2.0 ms-1.and the white ball continues to move in the same direction at 0.5 ms-1.as shown.

Before After

(i) Show that momentum is conserved

(ii) Find if Ek is conserved

(iii) What type of collision was it? 15. (a) A vehicle of mass 6 kg moving at 8 ms-1.collides with a vehicle of mass 8 kg moving at 5 ms-1.as

shown. They stick together.

Before After

What is the combined velocity? How much kinetic energy is lost?

(b) The same vehicles collide again but this time the velocity of the 8kg vehicle is reversed. Once again they stick together.

Before After

What is the combined velocity?

How much kinetic energy is lost?

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16. (a) A vehicle of mass 6 kg moving at 8 ms-1. collides with a vehicle of mass 8 kg moving at 5 ms-1.as shown. After the collision they separate.

Before After

What is the velocity of the 8kg mass?

How much kinetic energy is lost?

(b) The same vehicles collide again but this time the velocity of the 8 kg vehicle is reversed before the collision.

Before After

What is the velocity of the 8kg mass?

How much kinetic energy is lost? 17. A stationary small car (mass 500 kg) is stuck by another car of mass 1000 kg. The two cars lock together

and move 40 m before stopping. If the frictional force on the two vehicles locked together is 7.5 x 1 03 N, calculate:

(a) the deceleration of the two cars

(b) the speed at which the two cars moved off after the impact

(c) the speed of the sports car just before the impact 18. A clockwork car, of mass 200 g, is set on a plank that floats on a cushion of air. The mass of the plank is

500 g. If the car moves to the right with a speed of 0.40 ms-1.calculate the speed of the plank. 19. A roller coaster carriage of mass 500 kg rolls down a slope and collides with four identical carriages at the

foot of the slope, each carriage having a mass of 500 kg. When the carriage collides they automatically lock together and move off with a speed of 5 ms-1..

(a) Use the law of conservation of momentum to calculate the speed of the loaded carriage just before impact.

(b) Calculate the kinetic energy of the carriage just before impact.

(c) Find the height from which the carriage was released (assume there is no friction in the system).

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1. (2000)The momentum of a rock of mass 4kg is 12kg m s–1

The kinetic energy of the rock is A 6J

B 18J

C 36J

D 144 J

E 288J.

2. (2001)A rocket of mass 5.0kg is travelling horizontally with a speed of 200ms-1.when it explodes into two parts. One part of mass 3.0kg continues in the original direction with a speed of 100ms-1.. The other part also continues in this same direction. Its speed is A 400N

B 500N

C 800N

D 1800N

E 2600N

3. (1996) A field-gun fires a shell of mass 10kg with a velocity of 100ms-1 East The velocity of the field-gun just after firing the shell is A 0 ms-1

B 1 ms-1 East

C 1ms-1 West

D 10 ms-1 East

E 10 ms-1 West

4. (1998) A block of mass 1 kg slides along a fric-tionless surface at 10ms-1. and it collides with a stationary block of mass 10kg. After the collision, the first block rebounds at 5 ms-1. and the other one moves off at 1.5 ms-1. .

A

B

C

D

E

Momentum of system

Kinetic energy of system

Type of collision

conserved conserved elastic

conserved not conserved inelastic

conserved not conserved elastic

not conserved not conserved inelastic

not conserved not conserved elastic

Which row in the following table is correct?

Past exam questions: Momentum

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5. (1998) A football of mass 0.42 kg is thrown at a stationary student of mass 50.0 kg who is wearing roller blades, as shown in the diagram below. When the student catches the moving ball she moves to the right. The instantaneous speed immediately after she catches the ball is 010 ms-1. Calculate the speed of the ball just before it is caught.

Vehicle P, of mass 0.2 kg, is projected with a velocity of 0.5 ms-1.to the right along the linear air track. It collides with vehicle Q, of mass 0.3 kg, which is initially at rest. After the collision, the vehicles move in opposite directions. Vehicle Q moves off with a velocity of 0.4 ms-1 to the right. (a) Show that vehicle P rebounds with a speed of 0.1 ms-1.after the collision.

(b) Calculate the change in momentum of vehicle P as a result of the collision.

(c) During the collision, a timing device records the time of contact between the two vehicles as 0.06 s. (i) Calculate the average force acting on vehicle P during the collision.

(ii) Sketch a graph showing how the force on vehicle P could vary with time while the

two vehicles are in contact.

6. (1997) The diagram below shows two vehicles P and Q on a linear air track.

Linear air track

Air flow

2

2

3

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7. (1996) During a test on car safety, two cars as shown below are crashed together on a test track.

(a) Car A, which has a mass of 1200kg and is moving at 18.0 ms-1, approaches car B, which has a mass of 1000kg and is moving at 10.8 ms-1 , in the opposite direction. The cars collide head on, lock together and move off in the direction of car A. (i) Calculate the speed of the cars immediately after the collision. (ii) Show by calculation that this collision is inelastic. (b) During a second safety test, a dummy in a car is used to demonstrate the effects of a collision. During the collision, the head of the dummy strikes the dashboard at 20 ms-1 as shown below and comes to rest in 0.02 s. The mass of the head is 5 kg. (i) Calculate the average force exerted by the dashboard on the head of the dummy during the collision. (ii) If the contact area between the head and the dashboard is 5 X 10 -4 m2 , calculate the pressure which this force produces on the head of the dummy. (iii) The test on the dummy is repeated with an airbag which inflates during the collision. During the collision, the head of the dummy again travels forward at 20 ms-1 and is brought to rest by the airbag. Explain why there is less risk of damage to the head of the dummy when the airbag is used.

4

5

61

8. (1999) (a) State the law of conservation of linear momentum.

(b) The diagram shows a linear air track on which two vehicles are free to move. Vehicle A moves towards vehicle B which is initially at rest. A computer displays the speeds of the two vehicles before and after the collision.

The table of results below shows the mass and velocity of each vehicle before and after the collision.

(i) Use these results to show that the change in momentum of vehicle A is equal in size but opposite in direction to the change in momentum of vehicle B. (ii) Use the data in the table to show whether the collision is elastic or inelastic

Vehicle

Mass

Velocity before collision

Velocity after collision

A

0.75 kg

0.82 ms-1.to the right

0-40 ms-1.to the right

B

0.50 kg

0.00 ms-1.

0-63 ms -1. to the right

5

1

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9 . (2002) (a) A space vehicle of mass 2500kg is moving with a constant speed of 0.50 ms-1 in the direction shown. It is about to dock with a space probe of mass 1500kg which is moving with a constant speed in the opposite direction.

After docking, the space vehicle and space probe move off together at 0.20ms-1.in the original direction in which the space vehicle was moving.

Calculate the speed of the space probe before it docked with the space vehicle. (b) The space vehicle has a rocket engine which produces a constant thrust of 1000N. The space probe has a rocket engine which produces a constant thrust of 500N.

The space vehicle and space probe are now brought to rest from their combined speed of 0.20ms-1. (i) Which rocket engine was switched on to bring the vehicle and probe to rest? (ii) Calculate the time for which this rocket engine was switched on. You may assume that a negligible mass of fuel was used during this time.

(c) The space vehicle and space probe are to be moved from their stationary position at A and

brought to rest at position B, as shown.

Explain clearly how the rocket engines of the space vehicle and the space probe are used to complete this manoeuvre.

Your explanation must include an indication of the relative time for which each rocket engine must be fired.

You may assume that a negligible mass of fuel is used during this manoeuvre.

2

3

2

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10. (2003) Two ice skaters are initially skating together, each with a velocity of 2.2 ms-1 to the right as shown.

The mass of skater R is 54 kg. The mass of skater S is 38 kg. Skater R now pushes skater S with an average force of 130N for a short time. This force is in the same direction as their original velocity.

As a result, the velocity of skater S increases to 4.6ms-1 to the right (a) Calculate the magnitude of the change in momentum of skater S. (b) How long does skater R exert the force on skater S? (c) Calculate the velocity of skater R immediately after pushing skater S. (d) Is this interaction between the skaters elastic? You must justify your answer by calculation.

2 2 2 2 3

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Impulse 1. Draw a rough graph showing how the force exerted by a golf club on a golf ball varies with time. On the

same graph show how the force exerted by the same club on

(a) a steel ball bearing and

(b) a soft sponge ball would vary with time.

Comment on the differences.

Repeat the graphs showing how the force of the ball on the club varies with time. 2. Find the impulse when a force of 100 N is applied for 0.5 s. 3. Find the average force when a bat hits a ball for 0.1 s and gives it an impulse of 1500 Ns. 4. A dog catches a ball of mass of 0.2 kg in its mouth. It brings the ball to rest from a speed of 5ms-1.in a

time of 0.05 s. Find

(a) the impulse lost by the ball

(b) the average force the dog exerts on the ball. 5. If a car of mass 950 kg accelerates at 2 ms-2, what is the unbalanced force acting on it? If, after

acceleration for 10 seconds, it crashes into a wall and comes to rest in 0.5 seconds, find the average force of resistance and the impulse exerted.

6. How long will it take a force of 10 N to stop a mass of 2.5 kg that is moving at 20 ms-1.? 7. A trolley of mass 2 kg moving at 5 ms-1.collides elastically with an identical stationary trolley. If the

collision lasts for 0.1 s what is the average force on the stationary trolley? 8. A hammer head of mass 1 kg is moving at 3 ms-1.when it strikes a nail. If the rebound velocity is zero,

and the impulse lasts for 15 milliseconds, calculate the impulse and the average force exerted. 9. A ball of mass 0.5 kg is in contact with a player’s bat for 0.02 s and reaches a speed of 15 ms-1.. If the ball

is initially at rest, what is the average force exerted and what is the impulse? 10. A hose delivers a jet of water at a rate of 100 kgs-1.at a speed of 50 ms-1.. Estimate the force exerted on a

wall if the water jet hits the wall at right angles. Assume that the water does not bounce off the wall. 11. A jet engine takes in 20 kg of air per second at 100 ms-1.. After being compressed and heated, the air is

discharged at 500 ms-1.. Calculate the thrust of the engine. 12. A girl hits a volleyball of mass 0.3 kg that is approaching her at 6 ms-1.. She punches it away in the

opposite direction at 11 ms-1.. If the ball is in contact with her hand for 0.2 s, find the average force she exerts on the ball

65

13. A sports scientist is measuring the forces on a tennis racquet using the time of contact between the ball and the racquet. The tennis ball has a mass of 100g and hits the racquet with a velocity of -9ms-1.and re-bounds from it at 6ms-1.. The time of contact is measured as 0.04s.

(a) What is the change in momentum of the tennis ball?

(b) Calculate the impulse of the racquet on the ball.

(c) What is the average force on the ball from the racquet? The scientist knows that the force varies with the time as shown in the graph.

(d) What is the peak force exerted by the racquet on the ball?

14. A car fascia is designed so that it compresses on impact if a person’s head hits it. This prevents undue

injury to the driver or passenger. Two materials are being tested as the filling for the fascia. A is a dense, rigid foam whilst B is softer and more easily compressed.

(a) Sketch the force/time graph for each foam if they were to undergo identical accidents, the dummy’s head hitting the fascia with the same velocity each time.

(b) Explain why foam B is the more satisfactory at reducing the maximum force applied to the head of the dummy.

66

1. (2003) A car is designed with a "crumple-zone" so that the front of the car collapses during impact

The purpose of the crumple zone is to A decrease the driver's change in momentum per

second

B increase the driver's change in momentum per

second

C decrease the driver's final velocity

D increase he driver's total change in momentum

E decrease the driver's total change in

momentum.

2. (1996) The graph below shows the force which acts on an object over a time interval of 8 seconds.

The momentum gained by an object during this 8 seconds is

A 12 Ns

B 32 Ns

C 44 Ns

D 52 Ns

E 72 Ns

3. (1997) Many car manufacturers are now fitting airbags which inflate automatically during an accident, as shown below.

The purpose of the airbag is to protect the driver by

A reducing his change of momentum per sec ond

B increasing his change of momentum per

second

C reducing his final velocity

D reducing his total change in momentum

E increasing his total change in momentum.

4. (1997) The force acting on an object is measured and the results are stored in a computer. The force-time graph obtained from the computer is shown below.

What is the average force acting on the object during the 50 milliseconds?

A 15N

B 10N

C 8N

D 2.5N

E 1N

Past exam questions: Impulse

67

5. (1999) The graph below shows how the force, F, exerted on an object varies with time t.

The area under the graph represents the object's change of A acceleration

B velocity

C momentum

D kinetic energy

E potential energy.

68

6. (1998)The apparatus in the diagram is being used to investigate the average force exerted by a golf club on a ball. The club hits the stationary ball. Timer 1 records the time of contact between the club and the ball. Timer 2 records the time taken for the ball to pass through the light gate beam. The mass of the ball is 45.00 ±0.01 g. The time of the contact between club and ball is 0.005 ±0.001 s. The time for the ball to pass through the light gate beam is 0.060 ±0.001 s. The diameter of the ball is 24 ± 1 mm.

(a) (i) Calculate the speed of the ball as it passes through the light gate, (ii) Calculate the average force exerted on the ball by the golf club. (b) (i) Show by calculation which measurement contributes the largest percentage error in the final value of the average force on the ball. (ii) Express your numerical answer to (a)(ii) in the form final value ± absolute error.

3 3

69

7. (2000) The apparatus shown below is used to test concrete pipe

When the rope is released, the 15 kg mass is dropped and falls freely through a distance of 2.0 m on to the pipe. (a) In one test, the mass is dropped on to an uncovered pipe. (i) Calculate the speed of the mass just before it hits the pipe. (ii) When the 15 kg mass hits the pipe the mass is brought to rest in a time of 0.02 s. Calculate the size and direction of the average unbalanced force on the pipe. (b) The same 15kg mass is now dropped through the same distance on to an identical pipe which is covered with a thick layer of soft material. Describe and explain the effect this layer has on the size of the average unbalanced force on the pipe. (c) Two 15kg masses, X and Y, shaped as shown, are dropped through the same distance on to identical uncovered concrete pipes When the masses hit the pipes, the masses are brought to rest in the same time. Which mass causes more damage to a pipe? Explain your answer in terms of pressure.

5

2

2

70

Density 1. A block of iron has a mass of 40000 kg and a volume of 5 m3. What is its density? 2. What is the mass of a cylinder of aluminium with a volume of 2.5 m3? (The density of aluminium is 2700 kg m-3 ) 3. 1 kg of nitrogen gas is used to fill a balloon. If the density of nitrogen is 1.25 kg m-3, find the volume of

the balloon. 4. A tank measures 60 cm long and 40 cm wide. 72 kg of water are to be poured into the tank. How deep

will the water be ? (Density of water is 1000 kg m-3) 5. What will be the mass of air in a classroom with the following dimensions? length l5 m, breadth 10 m and height 4 m (The density of air is 1.3 kg m-3) 6. In the diagram opposite the piston contains 0.2 kg of

oxygen, which has a density of 1.43 kg m-3.

(a) If the plunger is at height of 40 cm, what is the cross-sectional area of the plunger ?

(b) The gas is heated and the plunger rises a further 20 cm. What is the density of the oxygen now?

7. A block cast from iron of density 9 gcm-3 measures 3 cm x 4 cm x 5 cm. When tested the mass of the

block was found to be 450 g, which tells the engineer it, contains an air bubble. Find the volume of the air bubble.

8. A tin contains 5 litres of paint has a mass of 7.2 kg.

(a) If the mass of the empty tin (plus lid) is 0.6 kg calculate the density of the paint.

(b) The metal used to make the tin has a density of 7800 kg m-3. Calculate the volume of metal used to make the tin and lid.

9. 0.01m3 of water is heated until it all changes to steam. What will be the approximate volume of the

steam? 10. A liquid is heated until it changes to a gas. What will happen to the spacing of the particles when the

substance changes from a liquid to a gas? 11. Describe an experiment to measure the density of air. Your answer should include:

(a) a diagram of the apparatus used

(b) a list of measurements taken

(c) any necessary calculations.

71

1. (2000) Density is measured in A N m-2

B N m-3

C kg m3

D kg m-2

E kg m-3

2. (2001) A block floats in water and two other liquids X and Y at the levels shown.

Which of the following statements is/are correct?

I The density of the material of the block is less than the density of water.

II The density of liquid X is less than the density of water.

III The density of liquid X is greater than the density of liquid Y.

A I only

B II only

C I and II only

D I and III only

E II and III only

2. (2003) A fixed mass of gas condenses at atmospheric pressure to form a liquid.

Which row in the table shows the approximate increase in density and the approximate decrease in spacing between molecules?

Approximate increase in

density

Approximate decrease in spacing between molecules

10 times

2 times

1 00 times

10 times

1000 times

10 times

1 000 000 times

100 times

1 000 000 times

1000 times

A

B

C

D

E

3. (1997) Which of the following gives the approximate relative spacings of molecules in ice, water and water vapour?

Molecular spacing in ice / units

Molecular spac-ing in water / units

Molecular spacing in wa-ter vapour / units

1 1 10

1 3 1

1 3 3

1 10 10

3 1 10

A

B

C

D

E

Past exam questions: Density

72

Pressure 1. Explain why the use of large tyres helps to prevent a tractor from sinking into soft ground. 2. A box weighs 120 N and has a base area of 2 m2. What pressure does it exert on the ground ? 3. If atmospheric pressure is 100 000 Pa, what force does the air exert on a wall of area 10 m2 ? 4. The surface area of the base of a block of wood is 2 m2. The weight of the block is 16000 N. Find the

pressure it exerts on the floor. 5. A force of 20 N is applied over an area of 5 cm2. What is the pressure? 6. The point of a pin has an area of 0.01mm2. If a force of 15 N is used to push the pin into a piece of wood,

find the pressure applied. 7. If the atmospheric pressure is 105 Pa and the area of the top of your head is 300 cm2, find the force exerted

on the top of your head by the air. 8. A book of weight 10 N applies a pressure 250 N to the table. Find the surface area of the book in contact

with the table. 9. A girl has a mass of 50 kg. When standing on one foot the area in contact with the floor is 150 cm2.

Find the pressure exerted. 10. A rectangular steel block measures 10 cm x 8 cm x 6 cm. What are the greatest and the least pressure that

it can exert on a surface ? (Density of steel is 8000 kg m-3) 11. A car has a mass of 750 kg. If the area of contact of each tyre with the road is 2.5 x 10-2 m2, find the

pressure applied to the road surface by the tyres. 12. If you want to rescue someone who has fallen through the ice on a pond, explain whether it would be safer

to walk or crawl across the ice towards them?

73

Pressure in Liquids 1. What is the pressure due to a depth of 10 m of water ? (Density of water = 1000 kg m-3). 2. A water tank has a base of cross-sectional area 0.5 m3 and a depth of water 1.5 m. Calculate

(a) the pressure at the bottom of the tank (caused by the water and by the pressure of the air above the water ).

(b) the resultant force on the base. 3. Water is supplied to flats from a tank on the roof. Find the extra water pressure to residents on the ground

floor if their taps are 30 m below the level the taps on the top floor. 4. A cube of side 12 cm is completely immersed in a liquid of density 800 kg m-3, so that the top surface is

horizontal and 20 cm below the surface of the liquid. Calculate the fluid pressure:

(a) at a depth of 20 cm

(b) at a depth of 32 cm.

(c) Hence calculate the force exerted on: (i) the top surface of the cube (ii) the bottom surface of the cube.

(d) Calculate the size and direction of the vertical force due to this pressure. 5. A cube of wood of sides 0.5 m floats in a large tank of water at a height of 0.3 m the surface. Calculate

(a) the weight of the cube

(b) the vertical upthrust given to the cube by the water

(c) the volume of water displaced by the cube.

(density of water = 1000 kg m-3; density of wood = 400 kg m-3) 6. The pressure, due to a liquid, at a depth of 6 m is 4.8 x 104 Pa

(a) P is at a depth of 4 m. Find the pressure at P.

(b) The pressure at Q is 7.2 x 104 Pa. Find the depth of Q.

74

1. (1996) An aircraft cruises at an altitude at which the air pressure is 0-4 X 105 Pa. The inside of the aircraft cabin is maintained at a pressure of 1 .0 x 105 Pa. The area of an external cabin door is 2 m2 .

What is the outward force produced on this door by the pressures stated?

A 0.3x105N

B 0.7xl05N

C 1.2x105N

D 2.0xl05N

E 2.8xl05N

3. (1998) Which pair of graphs correctly shows how the pressure produced by a liquid depends on the depth and the density of the liquid?

2. (1999)A spacecraft of mass 1200kg has landed on a planet where the gravitational field strength is 5Nkg-1. The spacecraft rests on three pads, each of contact area 0.5m2. The pressure exerted by these three pads on the surface of the planet is A 8.0xl02Pa

B 4.0xl03Pa

C 7-8xl03Pa

D 9.0xl03Pa

E l.2x104Pa.

Past exam questions: Pressure

75

4. (1998)T he rigid container of a garden sprayer has a total volume of 8-0 litres (8 X 10-3 m3 ). A gardener pours 5.0 litres (5 X 10-3 m3 ) of water into the container. The pressure of the air inside the container is 1.01 X 105 Pa.

(a) Calculate the mass of air in the sprayer. Use information from the data sheet.

(b) The gardener now pumps air into the container until the pressure of the air inside it becomes 3.0xl05Pa. (i) The area of the water surface in contact with the compressed air is 7.0 X 10-3 m2 . Calculate the force which the compressed air exerts on the water.

(ii) Water is now released through the nozzle. Calculate the final pressure of the air inside the sprayer when the volume of water falls from 5.0 litres (5 X 10-3 m ) to 2.0 litres (2 X 10 -3 m3). Assume the temperature of the compressed air remains constant

3 4

76

7. P, Q and R are at the same depth in three different liquids.

(a) The pressure, due to the liquid, is 3.6 x 103 Pa at Q. Find the pressure at R.

(b) The pressure is 3.0 x 103 Pa at P. Find the density of liquid A. 8. A sonar detector, of mass 60 kg, is used for monitoring the presence of dolphins. It is attached by a verti-

cal cable to the sea bed so that the detector is held below the surface of the sea.

(a) Explain the cause of the buoyancy force on the detector.

(b) Draw a diagram showing the buoyancy force and the other forces acting on the detector.

(c) If the buoyancy force has a value of 31500 N, what is the value of the tension in the cable attached to the sea bed?

Liquid B ρ=103 kgm-3

Liquid C ρ= 1.2x103 kgm-3 Liquid A

77

5. (2003) A tank of water rests on a smooth horizontal surface. (a) A student takes measurements of the pressure at various depths below the surface of the water, using the apparatus shown.

The pressure meter is set to zero before the glass tube is lowered into the water. (i) Sketch a graph to show how the pressure due to the water varies with depth below the surface of the water. (ii) Calculate the pressure due to the water at a depth of 0.25m below its surface. (iii) As the glass tube is lowered further into the tank, the student notices that some water rises inside the glass tube. Explain why this happens. (b) The mass of water in the tank is 2.7 X 103kg. The tank has a mass of 300kg and a flat rectangular base. The dimensions of the tank are shown in the diagram below. Atmospheric pressure is 1.01 x 105Pa.

Calculate the total pressure exerted by the base of the tank on the surface on which it rests.

4

3

78

1. (2002)A flat bottomed test-tube containing aluminium rivets is floated in liquid A.

Thebottom of the test-tube is at a depth of 5 cm below the surface.

The same test-tube and aluminium rivets are then floated in liquid B.

The bottom of the test-tube is at a depth of 8cm below the surface.

Which of the following statement(s) is/are true?

I In each liquid the pressure at the bottom of the test-tube is the same.

II The density of liquid A is greater than the density of liquid B.

III In each liquid the up thrust on the bot-tom of the test-tube is the same.

A I only

B II only

C I and II only

D II and III only

E I, II and III

2. (1997) A small metal block is suspended from a spring balance at a depth h below the surface of a liquid in a large beaker.

Which of the following statements is/are true?

I The reading on the spring balance depends on the density of the liquid in the beaker.

II The reading on the spring balance is equal to the upthrust of the liquid on the metal block.

Ill The reading on the spring balance will increase as the depth h is increased.

A I only

B II only

C III only

D I and II only

E I and III only

Past exam questions: Upthrust & pressure in a liquid

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3. (1999) (a) Sketch a graph which shows how the pressure caused by a liquid depends on the depth below the surface of the liquid. Numerical values are not required but the axes should be clearly labelled. (b) There is a buoyancy (upthrust) force on a submarine when it is submerged in sea water. (i) Explain fully how the buoyancy force is produced on the submarine. You may make reference to your graph from (a). (ii) The total volume of sea water displaced by the submarine is 14.5 m3 . Calculate the mass of sea water displaced by the submarine. (iii) The submarine changes depth by altering the mass of water stored in tanks in the submarine. Compressed air replaces some water in the tanks

Explain, in terms of the forces acting on the submarine, why replacing water in the tanks with compressed air causes the submarine to accelerate upwards.

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4. (2000)A sonar detector is attached to the bottom of a fresh water loch by a vertical cable as shown

The detector has a mass of 100kg. Each end of the detector has an area of 0.40m2. Atmospheric pressure is 101000 Pa. (a) The total pressure on the top of the detector is 108350 Pa. Show that the total pressure on the bottom of the detector is 111290 Pa. (b) Calculate the upthrust on the detector. (c) The sonar detector is now attached, as before, to the bottom of a sea water loch. The top of the detector is again 0.75 m below the surface of the water. How does the size of the upthrust on the detector now compare with your answer to (b)? You must justify your answer.

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Pressure and Volume (constant Temperature) 1. 100 cm3 of air is contained in a syringe at atmospheric pressure (105 Pa). If the volume is reduced firstly

to 50 cm3 and then 20 cm3 without a change in temperature, what will be the new pressures? 2. If the piston in a cylinder containing 300 cm3 of gas at a pressure of 105 Pa is moved outwards so that the

pressure of the gas falls to 8 x 104 Pa, find the new volume of the gas.

3. A weather balloon contains 80 m3 of helium at normal atmospheric pressure of 105 Pa. What will be the

volume of the balloon at an altitude where the air pressure is 6.8 x 104 Pa.

4. A balloon filled with hydrogen gas is released from sea level. As the balloon rises it expands in volume.

It is designed to burst when the volume becomes 4 times its original volume at sea level.

When the balloon leaves sea level, its volume is 3.0 m3 and the pressure is 100 kPa. What is the pressure inside the balloon when it is just about to burst, assuming its temperature remains constant?

5. Part of the suspension system of a car operates by compression of a gas sealed in a rubber container. The

volume of gas in the container is normally 1 x 10-3 m3, at a pressure of 2 x 105 Pa, but when the car hits a

large stone in the road the gas is compressed to a volume of 0.5 x 10-3 m3. What is the pressure inside the container when compressed, assuming no change in temperature occurs?

6. Flasks X, Y and Z have the same volumes. Y contains air at a pressure of 6 atmospheres. X and Z have

been evacuated and the taps are closed. Tap 1 is now opened, followed a short time later by Tap 2.

Assuming that the temperature changes are negligible, find

(a) the pressure in flask Y with only tap 1 open.

(b) the pressure in flask Y when both taps 1 and 2 are opened.

(1 atmosphere = 105 Pa) 7. A skin diver, operating at a pressure of 2.5 x 105 Pa, carries his air supply in a steel cylinder on his back.

When full, the cylinder contains 0.060 m3 of air at a pressure of 1.6 x 107 Pa. Calculate

(a) the volume of air available to him at this depth;

(b) the time that the air would last if he requires air at a flow rate of 0.30 m3 per minute.

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8. A sample of air is enclosed within a cylinder by a move-able piston of diameter 10 cm. The mass of the piston is 2 kg. If the atmospheric pressure is 105 Pa find the pres-sure of the enclosed air.

Masses are added to the piston and the piston moves down until it is 2 cm from the end of the cylinder.

Find the new pressure and hence the additional mass added.

9. A diver uses a cylinder of compressed air that holds 15 litres of air at a pressure of 1.2 x 105 Pa.

(a) Calculate the volume this air would occupy at a depth where the pressure is 200 kPa. (b) If the diver breathes 25 litres of air each minute at this pressure, calculate how long the diver could remain at this depth. (Assume that all the air from the cylinder is available.)

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Pressure and Temperature (constant Volume) 1. (a) Change the following Celsius temperatures into Kelvin temperatures, (i) -273 oC (ii) -150 oC (iii) -50 oC (iv) 0 oC (v) 27 oC (vi) 150 oC (vii) 300 oC

(b) Change the following Kelvin temperatures into Celsius temperatures, (i) 0 K (ii) 23 K (iii) 100 K (iv) 293 K (v) 350 K (vi) 373 K (vii) 500 K 2. The air pressure in a car tyre is 2.8 x 105 Pa when the temperature is 17 oC. After a long journey the

pressure has risen to 3.2 x 105 Pa. Calculate the new air temperature. (Assume volume remains constant.)

Explain in terms of the kinetic model why the pressure has increased. 3. A cylinder of oxygen at 27 oC has a pressure of 3 x 106 Pa. What will be the new pressure if the gas is

cooled to 0 oC? 4. An electric light bulb is designed so that the pressure of the inert gas inside it is 100 kPa (normal air

pressure) when the temperature of the bulb is 350 oC. At what pressure must the bulb be filled if this is done at 15 oC?

5. A compressed air tank that at room temperature of 27 oC normally contains air at 4 atmospheres, is fitted

with a safety valve that operates at 10 atmospheres. During a fire the safety valve was released. Calculate the average temperature of the air in the tank when this happened.

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Temperature and Volume (constant Pressure) 1. 100 cm3 of a fixed mass of air is at a temperature of 0 °C. If its pressure remains constant at what

temperature will the volume be 110 cm3. 2. Air is trapped in a glass capillary tube by a bead of mercury. The volume of air is found to be 0.10 cm3 at

a temperature of 27 °C. Calculate the volume of air at a temperature of 87 °C. 3. The volume of a fixed mass of gas at constant temperature is found to be 50 cm3. The pressure remains

constant and the temperature doubles from 20 °C to 40 °C. Explain why the new volume of the gas is not 100 cm3.

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General Gas Equation 1. Some gas at room temperature and a pressure of 100 kPa was trapped in a syringe by sealing the nozzle.

(a) The plunger was depressed and the gas allowed to return to room temperature. The volume was found to have been halved. What was the new pressure?

(b) In another experiment the pressure of the gas was kept constant. The temperature of the gas was 300 K (27 oC). To what temperature would the gas have to be heated to double its volume?

2. A sample of air is enclosed within a cylinder by a moveable piston. The initial conditions are as shown.

(a) The piston is pushed in until the volume is reduced to 20 cm3. Find the new pressure assuming no temperature change. Explain the change in pressure in terms of the kinetic model.

(b) The piston is held at the new position and the temperature increased to 200 oC. Find the new pressure of the air.

3. A sealed syringe contains 100 cm3 of air at atmospheric pressure 105 Pa and a temperature of 27 °C.

When the piston is depressed the volume of air is reduced to 20 cm3 producing a temperature rise of 4 °C. Calculate the new pressure of the gas.

4. Calculate the effect the following changes have on the pressure of a fixed mass of gas.

(a) Its temperature (in K) doubles and volume halves.

(b) Its temperature (in K) halves and volume halves.

(c) Its temperature (in K) trebles and volume quarters. 5. Calculate the effect the following changes have on the volume of a fixed mass of gas.

(a) Its temperature (in K) doubles and pressure halves.

(b) Its temperature (in K) halves and pressure halves.

(c) Its temperature (in K) trebles and pressure quarters. 6. Explain the pressure-volume, pressure-temperature and volume-temperature laws qualitatively in terms of

the kinetic model.

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1. (2000) The pressure of a fixed mass of gas is 100kPa at a temperature of -52 °C. The volume of the gas remains constant. At what temperature would the pressure of the gasbe200kPa?

A -26°C

B +52°C

C +147°C

D +169°C

E +442°C

2. (2000) The end of a bicycle pump is sealed with a stopper so that the air in the chamber is trapped.

The plunger is now pushed in slowly caus-ing the air in the chamber to be compressed. As a result of this the pressure of the trapped air increases. Assuming that the temperature remains con-stant, which of the following explain/s why the pressure increases?

I The air molecules increase their average speed.

II The air molecules are colliding more of-ten with the walls of the chamber.

Ill Each air molecule is striking the walls of the chamber with greater force.

A II only

B III only

C I and II only

D I and III only

E I, II and III

3. (2001) Ice at -10°C is heated until it becomes water at 80°C. The temperature change on the kelvin scale is A 70 K

B 90 K

C 343 K

D 363 K

E 636 K.

4. (2002) A sealed hollow buoy drifts from warm Atlantic waters into colder Arctic waters. The volume of the buoy remains constant. The pressure of the air trapped inside the buoy changes. This is because the pressure of the trapped air is A directly proportional to the kelvin temperature

B inversely proportional to the kelvin

temperature

C inversely proportional to the volume of the air

in the buoy

D inversely proportional to the Celsius

temperature

E directly proportional to the celsius

temperature.

5. (1999) A girl wrote the following statements in her physics notebook.

I The pressure of a fixed mass of gas varies inversely as its volume, provided the temperature of the gas remains constant.

II The pressure of a fixed mass of gas varies directly as its kelvin temperature, provided the volume of the gas remains constant.

Ill A temperature change of 20 °C in a gas is the same as a temperature change of 293 K.

Which of the above statements is/are correct?

A I only

B II only

C III only

D I and II only

E II and III only

Past exam questions: Gas Law

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6. (2003) A rigid metal cylinder stores compressed gas. Gas is gradually released from the cylinder. The temperature of the gas remains constant.

Which set of graphs shows how the pressure, the volume and the mass of the gas in the cylinder change with time?

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7 (1998) The pressure-volume graph below describes the behaviour of a constant mass of gas when it is heated.

Which of the following shows the corresponding pressure-temperature graph?

8. (1999) On a cold morning, a motorist checks the pressure of the air in one of her car tyres. It is found to be 3-0 X 105Pa at a temperature of 2°C. After a long run on a motorway, the temperature of the air in the tyre rises to 57 °C. The volume of the air in the tyre remains constant and no air es-capes. Which row in the following table gives the correct value of the final pressure of the air in the tyre and a correct statement about the final density of the air in the tyre compared to the initial density?

Final pressure of air Final density of air

8.6xl06Pa greater

8.6xl06Pa same

8.6xl06Pa less

3.6xl05Pa same

3.6xl05Pa less

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B

C

D

E

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9. (1999) Gas is often stored in cylinders at high pressure. The pressure of the gas must be reduced by a reduction valve before the gas can be used.

The pressure of the gas in the cylinder is 20 x 105Pa. The pressure of the gas as it leaves the reduction valve is 4 x 10s Pa.

Gas with a volume of 0.01m3 enters the reduction valve from the cylinder. What is the volume of this gas when it leaves the reduction valve, assuming that the temperature of the gas does not change?

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10. (1997) A pupil uses the apparatus shown in the diagram to investigate the relationship between the pressure and the temperature of a fixed mass of gas at constant volume . The cylinder is fully immersed in a beaker of water and the water is slowly heated. You may assume that the volume of the cylinder does not change as the temperature of the water changes. (a) Explain why the cylinder must be fully immersed in the beaker of water. (b) The pressure of the gas in the cylinder is 100 kPa when the gas is at a temperature of 17°C. Calculate the pressure of the gas in the cylinder when the temperature of the gas is 75 °C. (c) The base of the cylinder has an area of 0-001 m . What is the force exerted by the gas on the base when the temperature of the gas is 75 °C? (d) What happens to the density of the gas in the cylinder as the temperature increases from 17 0C to 75°C? Justify your answer.

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11. (2001) (a) In an experiment to find the density of air, a student first measures the mass of a flask full

of air as shown below.

The air is now removed from the flask and the mass of the evacuated flask measured. This procedure is repeated a number of times and the following table of measurements is obtained.

The volume of the flask is measured as 2.0 X 10-3 m3. (i) Copy and complete the bottom row of the table. (ii) Calculate the mean mass of air removed from the flask and the random uncertainty in this mean. Express the mean mass and the random uncertainty in kilograms. (iii) Use these measurements to calculate the density of air. (iv) Another student carries out the same experiment using a flask of larger volume.

Explain why this is a better design for the experiment. (b) The cylinder of a bicycle pump has a length of 360mm as shown in the diagram. The outlet of the pump is sealed. The piston is pushed inwards until it is 160mm from the outlet.

The initial pressure of the air in the pump is 1.0 x 105 Pa. (i) Assuming that the temperature of the air trapped in the cylinder remains constant, calculate the final pressure of the trapped air. (ii) State one other assumption you have made for this calculation. (iii) Use the kinetic model to explain what happens to the pressure of the trapped air as its volume

Experiment number 1 2 3 4 5 6

Mass of flask and air /kg 0.8750 0.8762 0.8748 0.8755 0.8760 0.8757 Mass of evacuated flask/kg 0.8722 0.8736 0.8721 0.8728 0.8738 0.8732

Mass of air removed /kg

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12. (2002) A technician designs the apparatus shown in the diagram to investigate the relationship between the temperature and pressure of a fixed mass of nitrogen which is kept at a constant volume.

(a) The pressure of the nitrogen is 109kPa when its temperature is 15°C. The temperature of the nitrogen rises to 45 °C. Calculate the new pressure of the nitrogen in the flask. (b) Explain, in terms of the movement of gas molecules, what happens to the pressure of the nitrogen as its temperature is increased. (c) The technician has fitted a safety valve to the apparatus. A diagram of the valve is shown below The piston of cross-sectional area 4-0 x 10-6 m2 is attached to the spring. The piston is free to move along the tube.

The following graph shows how the length of the spring varies with the force exerted by the nitrogen on the piston. (see next page for graph)

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(i) Calculate the force exerted by the nitrogen on the piston when the reading on the pressure gauge is 1.75 X 105Pa. (ii) What is the length of the spring in the safety valve when the pressure of the nitrogen is 1.75 X 105Pa? (d) The technician decides to redesign the apparatus so that the bulb of the thermometer is placed inside the flask. Give one reason why this improves the design of the apparatus.

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