AQA GCSE Physics 2-3 Work, Energy & Momentum GCSE Physics pages 146 to 159 July 2010

AQA GCSE Physics 2-3

Work, Energy & Momentum

GCSE Physics pages 146 to 159

July 2010

AQA GCSE Specification

WORK & ENERGY12.3 What happens to the movement energy whenthings speed up or slow down?

Using skills, knowledge and understanding of how science works:• to discuss the transformation of kinetic energy to other forms of energy in particular situations.

Skills, knowledge and understanding of how science works set in the context of:• When a force causes a body to move through a distance, energy is transferred and work is done.• Work done = energy transferred.• The amount of work done, force and distance are related by the equation:work done = force applied × distance moved in direction of force• Work done against frictional forces is mainly transformed into heat.• Elastic potential is the energy stored in an object when work is done on the object to change its shape.• The kinetic energy of a body depends on its mass and its speed.HT Calculate the kinetic energy of a body using the equation:kinetic energy = ½ × mass × speed2

MOMENTUM12.4 What is momentum?

Using skills, knowledge and understanding of how science works:

• to use the conservation of momentum (in one dimension) to calculate the mass, velocity or momentum of a body involved in a collision or explosion

• to use the ideas of momentum to explain safety features.

Skills, knowledge and understanding of how science works set in the context of:

• Momentum, mass and velocity are related by the equation:

momentum = mass × velocity• Momentum has both magnitude and direction.• When a force acts on a body that is moving, or able to

move, a change in momentum occurs.• Momentum is conserved in any collision/explosion

provided no external forces act on the colliding/exploding bodies.

HT Force, change in momentum and time taken for the change are related by the equation:

force = change in momentum / time taken for the change

WorkWhen a force causes a body to move through a distance, energy is transferred and work is done.

Work done = energy transferred.

Both work and energy are measured in joules (J).

Work and frictionWork done against frictional forces is mainly transformed into heat.

Rubbing hands together causes them to become warm.

Brakes pads become hot if they are applied for too long. In this case some of the car’s energy may also be transferred to sound in the form of a ‘squeal’

The work equationThe amount of work done, force and distance are related by the equation:

work done = force applied × distance moved in the direction

of the force

Work is measured in joules (J)Force is measured in newtons (N)Distance is measured in metres (m)

also:

force = work done ÷ distance moved

and:

distance = work done ÷ force

force distance

work

Question 1Calculate the work done when a force of 5 newtons moves through a distance of 3 metres.

work = force x distance

= 5N x 3m

work = 15 joules

Question 2

Calculate the work done when a force of 6 newtons moves through a distance of 40 centimetres.


= 6 N x 40 cm

= 6 N x 0.40 m

work = 2.4 joules

Question 3

Calculate the value of the force required to do 600 joules of work over a distance of 50 metres.


becomes:

force = work done ÷ distance

= 600 J ÷ 50 m

force = 12 newtons

Question 4Calculate the distance moved by a force of 8 newtons when it does 72 joules of work.


becomes:

distance = work done ÷ force

= 72 J ÷ 8 N

distance moved = 9 metres

Question 5Calculate the work done by a child of weight 300N who climbs up a set of stairs consisting of 12 steps each of height 20cm.


The child must exert an upward force equal to its own weight.

Therefore: force = 300N

This force is exerted upwards and so the distance must also be measured upwards.

= (12 x 20cm)

= 2.4m

therefore:

work = 300 N x 2.4 m

work = 720 J

Question 6Calculate the work done by a person of mass 80kg who climbs up a set of stairs consisting of 25 steps each of height 10cm.


the person must exert an upward force equal their weight

the person’s weight = (80kg x 10N/kg) = 800N

the distance moved upwards equals (10 x 25cm) = 2.5m

work = 800 N x 2.5 m

work = 2000 J

Completework force distance

J 50 N 3 m

800 J N 20 m

500 J 250 N m

kJ 4000 N 2 m

2 MJ 3.03 N 5 km

150

40

2

80

400

Answers

Choose appropriate words to fill in the gaps below:

Work is done when a _______ moves through a distance.

The amount of _______ transferred is also equal to the work done. When a car brakes energy is transformed to ______.

Work done is ______ to the force _________ by the distance moved in the __________ of the force. The work done is measured in ______ if the force is measured in newtons and the _________ in metres.

multiplied distance joulesequalforceenergy direction

WORD SELECTION:

heat

multiplied

distance

joules

equal

force

energy

direction

heat

Energy and workNotes questions from pages 146 & 147

1. What is meant by ‘work’?2. Copy both of the equations for work on page

146 along with the units used.3. Copy and answer questions (a) and (b) on

pages 146 and 147.4. Explain two ways in which the force of friction

causes energy to be transformed into heat.5. Copy the Key Points on page 147.6. Answer the summary questions on page 147.

Energy and work ANSWERS

In text questions:

(a) To the surroundings as heat energy and sound energy

(b) 300 J

Summary questions:

1. (a) 96 J

(b) 96 J

2. (a) (i) 90 J

(ii) 4500 J

(b) 0.60 m

Potential energyElastic potential energy is the energy stored in an object when work is done on an object to change its shape.

An elastic object regains its shape after being stretched or squashed. Elastic potential energy is

stored in the bow string when it is pulled by the archer.

Gravitational potential energy is the energy stored in an object when work is done in moving the object upwards.

The potential energy stored is equal to the weight of the object multiplied by the height lifted.

The weightlifter stores gravitational potential energy when he lifts the weights.

Kinetic energy

Kinetic energy is the energy possessed by a body because of its speed and mass.

kinetic energy = ½ x mass x (speed)2

kinetic energy is measured in joules (J)mass is measured in kilograms (kg)speed is measured in metres per second (m/s)

Question 1Calculate the kinetic energy of a car of mass 1000kg moving at 5 m/s.


kinetic energy = ½ x 1000kg x (5m/s)2

kinetic energy = ½ x 1000 x 25kinetic energy = 500 x 25kinetic energy = 12 500 joules

Question 2

Calculate the kinetic energy of a child of mass 60kg moving at 3 m/s.


k.e. = ½ x 60kg x (3m/s)2

k.e. = ½ x 60 x 9

k.e. = 30 x 9

kinetic energy = 270 J

Question 3Calculate the kinetic energy of a apple of mass 200g moving at 12m/s.


k.e. = ½ x 200g x (12m/s)2

k.e. = ½ x 0.200kg x 144

k.e. = 0.100 x 144

kinetic energy = 14.4 J

Question 4Calculate the mass of a train if its kinetic energy is 2MJ when it is travelling at 4m/s.


2MJ = ½ x mass x (4m/s)2

2 000 000J = ½ x mass x 162 000 000 = 8 x mass2 000 000 ÷ 8 = mass mass = 250 000 kg

Question 5Calculate the speed of a car of mass 1200kg if its kinetic energy is 15 000J.


15 000J = ½ x 1200kg x (speed)2

15 000 = 600 x (speed)2

15 000 ÷ 600 = (speed)2

25 = (speed)2

speed = 25

speed = 5 m/s

Question 6Calculate the speed of a ball of mass 400g if its kinetic energy is 20J.


20J = ½ x 400g x (speed)2

20 = ½ x 0.400kg x (speed)2

20 = 0.200 x (speed)2

20 ÷ 0.200 = (speed)2

100 = (speed)2

speed = 100speed = 10 m/s

Completekinetic energy mass speed

J 4 kg 2 m/s

27 J kg 3 m/s

1000 J 80 kg m/s

kJ 200 kg 8 m/s

3.2 J 3.03g 4 m/s

8

6

5

6.4

400

Answers


Elastic ________ energy is the energy stored when an object is stretched or ________. This energy is released when the object ________ to its original shape.

Kinetic energy is the energy possessed by an object due to its _______ and mass. If the mass of an object is ________ its kinetic energy doubles. If the speed is doubled the kinetic energy will increase by ______ times.

When a __________ elastic band is released elastic potential energy is converted into _________ energy.

doubledkinetic stretchedreturns potential squashedfour

WORD SELECTION:

speed

doubled

kinetic

stretched

returns

potential

squashed

four

speed

Kinetic energyNotes questions from pages 148 & 149

1. How can gravitational potential energy be calculated? (see the practical on page 148)

2. Copy the equation for kinetic energy at the top of page 149 along with the units used.

3. Repeat the calculation below the kinetic energy equation but this time with a mass of 400 kg moving at a speed of 8 m/s.

4. What does ‘elastic’ mean? 5. What is elastic potential energy?6. Copy and answer question (b) on page 149.7. Copy the Key Points on page 149.8. Answer the summary questions on page 149.

Kinetic energy ANSWERS

In text question:(b) Heat energy transferred to the surroundings, the foot and the shoe; also sound energy.

Summary questions:1. (a) (i) Chemical energy from the loader is

transferred into elastic potential energy of the catapult and some is wasted as heat energy.

(ii) Elastic potential energy in the catapult is transformed into kinetic energy of the object and the rubber band and heat energy (plus a little sound energy).

(b) (i) 10 J (ii) 10 J

2. (a) 3800 N (b) Friction due to the brakes transforms it

from kinetic energy of the car to heat energy in the brakes.

(c) 800 kg

Momentum

momentum = mass x velocity

mass is measured in kilograms (kg)

velocity is measured in metres per second (m/s)

momentum is measured in:

kilogram metres per second (kg m/s)

Momentum has both magnitude and direction.

Its direction is the same as the velocity.

The greater the mass of a rugby player the greater is his momentum

Question 1Calculate the momentum of a rugby player, mass 120kg moving at 3m/s.

momentum = mass x velocity = 120kg x 3m/s

momentum = 360 kg m/s

Question 2Calculate the mass of a car that when moving at 25m/s has a momentum of 20 000 kg m/s.

momentum = mass x velocity becomes: mass = momentum ÷ velocity = 20000 kg m/s ÷ 25 m/s

mass = 800 kg

Completemomentum mass velocity

kg m/s 50 kg 3 m/s

160 kg m/s kg 20 m/s

1500 kg m/s 250 kg m/s

kg m/s 500 g 8 m/s

3 kg m/s kgkg 50 cm/s

150

8

6

4

6

Answers

Momentum conservation

Momentum is conserved in any collision or explosion provided no external forces act on the colliding or exploding bodies.

The initial momentum of the yellow car has been conserved and transferred to the red car

Question 1

A truck of mass 0.5kg moving at 1.2m/s collides and remains attached to another, initially stationary truck of mass 1.5kg. Calculate the velocity of the trucks after the collision.

total momentum before collisionmomentum = mass x velocity 0.5 kg truck: = 0.5 kg x 1.2 m/s = 0.6 kg m/s1.5 kg truck: = 1.5 kg x 0 m/s = 0 kg m/stotal initial momentum = 0.6 kg m/sMomentum is conserved in the collisionso total momentum after collision = 0.6 kg m/stotal momentum = total mass x velocity0.6 kg m/s = 2.0 kg x velocity0.6 ÷ 2.0 = velocityvelocity = 0.3 m/s

Question 2

A train wagon of mass 800 kg moving at 4 m/s collides and remains attached to another wagon of mass 1200 kg that is moving in the same direction at 2 m/s. Calculate the velocity of the wagons after the collision.

total momentum before collisionmomentum = mass x velocity 800 kg wagon: = 800 kg x 4 m/s = 3200 kg m/s1200 kg truck: = 1200 kg x 2 m/s = 2400 kg m/stotal initial momentum = 5600 kg m/sMomentum is conserved in the collisionso total momentum after collision = 5600 kg m/stotal momentum = total mass x velocity5600 kg m/s = 2000 kg x velocity5600 ÷ 2000 = velocityvelocity = 2.8 m/s


The momentum of an object is equal to its ______ multiplied by its velocity. Momentum has _________, the same as the velocity, and is measured in kilogram _______ per second.

In any interaction of bodies, where no external _______ act on the bodies, __________ is conserved.

In snooker, a head-on collision of a white ball with a red ball can result in the red ball moving off with the ______ initial velocity of the white ball. This is an example of momentum ____________.

momentum

forces

metres mass

direction same

WORD SELECTION:

conservation

momentum

forces

metres

mass

direction

same

conservation

MomentumNotes questions from pages 214 & 215

1. What is ‘momentum’?2. Copy out the equation at the top of page 214. State the

units for each quantity in the equation.3. Copy and answer question (a) on page 214.4. Under a heading “Conservation of momentum” copy

out the statement in bold at the bottom of page 214. 5. Copy out the worked example on page 215.6. Copy and answer question (b) on page 215.7. Copy the Key Points on page 215.8. Answer the summary questions on page 215.

Momentum ANSWERS

In text questions:

(a) 240 kg m/s

(b) 0.48 m/s

Summary questions:

1. (a) mass, velocity

(b) momentum, force

2. (a) 5000 kg m/s

(b) velocity

= momentum / mass

= 5000 / 2500

= 2.0 m/s

Head-on collisionsIn this case bodies are moving in opposite directions.

Momentum has direction.

One direction is treated as positive, the other as negative.

In calculations the velocity of one of the colliding bodies must be entered as a NEGATIVE number.

+ ve velocity

- ve velocity

NEGATIVE POSITIVEDIRECTION OF MOTION

Question 1

A car of mass 1000 kg moving at 20 m/s makes a head-on collision with a lorry of mass 2000 kg moving at 16 m/s. Calculate their common velocity after the collision if they remain attached to each other.


car, mass 1000kglorry, mass 2000kg

16 m/s20 m/s

total momentum before collisionmomentum = mass x velocity car: = 1000 kg x +20 m/s = +20000 kg m/slorry: = 2000 kg x -16 m/s = -32000 kg m/stotal initial momentum = -12000 kg m/sMomentum is conserved in the collisionso total momentum after collision = -12000 kg m/stotal momentum = total mass x velocity-12000 kg m/s = 3000 kg x velocity-12000 ÷ 3000 = velocitycommon velocity = - 4 m/sThe lorry/car combination will move in the negative direction (to the left in this case) with a common velocity of 4 m/s.

Question 2

A car of mass 1000 kg moving at 30 m/s makes a head-on collision with a lorry of mass 2000 kg moving at 15 m/s. Calculate their common velocity after the collision if they remain attached to each other.


car, mass 1000kglorry, mass 2000kg

15 m/s30 m/s

total momentum before collisionmomentum = mass x velocity car: = 1000 kg x +30 m/s = +30000 kg m/slorry: = 2000 kg x -15 m/s = -30000 kg m/s

total initial momentum = 0 kg m/s

Momentum is conserved in the collision

so total momentum after collision = 0 kg m/s

The lorry/car combination will not move after the collision.

Explosions

Before an explosion the total momentum is zero.

As momentum is conserved, the total momentum afterwards must also be zero.

This means that the different parts of the exploding body must move off in different directions.

Question 1

An artillery gun of mass 1500kg fires a shell of mass 20kg at a velocity of 150m/s. Calculate the recoil velocity of the gun.

NEGATIVE

POSITIVE

DIRECTION OF MOTION

shell, mass 20kg

150 m/s

recoil

artillery gun, mass 1500kg

The total momentum before and after the explosion is ZEROmomentum = mass x velocity shell: = 20 kg x +150 m/s = +3000 kg m/s

This must cancel the momentum of the gun.Therefore the gun’s momentum must be -3000 kg m/sgun: = 1500 kg x recoil velocity = -3000 kg m/s

recoil velocity = - 3000 ÷ 1500= - 2m/s

The gun will recoil (move to the left)

with a velocity of 2 m/s.

Question 2A girl of mass 60kg throws a boy, mass 90kg out off a swimming pool at a velocity of 2m/s. What is the girl’s recoil velocity?


recoil

girl, mass 60kg

2 m/s

boy, mass 90kg

recoil

girl, mass 60kg

2 m/s

boy, mass 90kg

The total momentum before and after throwing the boy is ZEROmomentum = mass x velocity boy: = 90 kg x +2 m/s = +180 kg m/s

This must cancel the momentum of the girl.Therefore the girl’s momentum must be -180 kg m/sgun: = 60 kg x recoil velocity = -180 kg m/s

recoil velocity = - 180 ÷ 60= - 3m/s

The girl will recoil (move to the left)

with a velocity of 3 m/s.

More on collisions and explosionsNotes questions from pages 152 & 153

1. Apart from size what other property does momentum have?

2. Copy and answer question (a) on page 152.3. Explain how conservation of momentum

applies in an explosion.4. Why do guns recoil?5. Copy and answer question (b) on page 153.6. Copy the Key Points on page 153.7. Answer the summary questions on page 153.

More on collisions and explosions ANSWERS

In text questions:

(a) The boat and the person who jumps off move away with equal and opposite amounts of momentum.

(b) 25 m/s

Summary questions:

1. (a) momentum

(b) velocity

(c) force

2. (a) 60 kg m/s

(b) 1.5 m/s

Force and momentum

A force will cause the velocity of an object to change and therefore also its momentum.

The greater the force the faster the momentum changes.

force is measured in newtons (N)

change in momentum is measured in:

kilogram metres per second (kg m/s)

time is measured in seconds (s)

force = time taken for the change

change in momentum

Equation proof

acceleration = velocity change ÷ time taken

multiplying both sides of this equation by ‘mass’

gives:

(mass x acceleration) = (mass x velocity) change ÷ time

but:

(mass x acceleration) = force

and:

(mass x velocity) = momentum

therefore:

force = momentum change ÷ time taken

Question 1

Calculate the force required to change the momentum of a car by 24000 kgm/s over a 6 second period.

force = momentum change ÷ time taken

= 24000 kgm/s ÷ 6 s

force = 4000N

Question 2

Calculate the time taken for a force of 6000N to cause the momentum of truck to change by 42000 kgm/s.force = momentum change ÷ time takenbecomes:time taken = momentum change ÷ force= 42000 kgm/s ÷ 6000 Nforce = 7 seconds

Completeforce momentum

changetime taken

N 8000 kgm/s 40 s

25 N kgm/s 20 s

500 N 3000 kgm/s s

N 8000 kgm/s 10 s

4 N kgm/s 2 minutes

200

500

6

800

480

Answers

Car safety features

Crumple zones, air bags and a collapsible steering wheel are designed to increase the time taken for a driver or passenger to change momentum to zero during a crash.

The equation: force = momentum change ÷ time taken

shows that if the time taken is increased for the same momentum change the force exerted is decreased so is the injury to the driver or passenger.

Playground flooring question

The picture shows rubber tiles used for playground flooring. Explain how these can reduce injury to children.

ANSWER:

When a child falls to the floor its momentum changes from a high value to zero.

The rubber flooring tiles increase the time taken for this change.

force = change in momentum ÷ time taken for the change

Therefore the force on the child is reduced and so is the potential injury.


The force exerted on an object is equal to the __________ change caused divided by the ______ taken for the change.

An airbag activates during a car _______. The inflated airbag _________ the time taken for a driver’s or passenger’s ________ to fall to zero. The time taken for their momentum to fall to ______ is also increased. Therefore the _______ exerted on the driver or passenger is __________ and so is the potential ________ caused.

velocity

increases

zero

crash

momentumtime force

WORD SELECTION:

decreased injury

velocity

increases

zero

crash

momentum

time

force

decreased injury

Changing momentumNotes questions from pages 154 & 155

1. What is the purpose of a car’s crumple zones?

2. Copy the key points on page 155.

3. Copy and answer questions (a), (b) and (c) on pages 154 and 155.

4. Copy the Key Points on page 155.

5. Answer the summary questions on page 155.

Changing momentum ANSWERS

In text questions:

(a) If a child falls off a swing, the rubber mat reduces the impact force by increasing the impact time when the child hits the ground.

(b) The force is bigger

(c) 1800 N

Summary questions:

1. (a) stays the same

(b) increases

(c) decreases

2. (a) 24 000 kg m/s

(b) (i) 2000 N

(ii) 800 N

Virtual Physics Laboratory SimulationsNOTE: Links work only in school

Roller Coaster.exe - Energy considerations

Online SimulationsWork (GCSE) - Powerpoint presentation by KT Kinetic Energy (GCSE) - Powerpoint presentation by KT Gravitational Potential Energy (GCSE) - Powerpoint presentation by KT Energy Skate Park - Colorado - Learn about conservation of energy with a skater dude! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. You can also take the skater to different planets or even space!

Rollercoaster Demo - Funderstanding Energy conservation with falling particles - NTNU Ball rolling up a slope - NTNU Pulley System - Fendt BBC AQA GCSE Bitesize Revision: Work, force and distance Potential and kinetic energy Kinetic energy equation

http://www.ktaggart.co.uk/physics/PowerPoint/Work.ppt

Forces for safety Notes questions from pages 156 & 157

1. Answer questions 1 and 2 on pages 156 and 157.

Forces for safety ANSWERS

1. The air bag increases the time taken to stop the person it acts on. This reduces the force of the impact. Also, the force is spread out across the chest by the air bag so its effect is lessened again.

2. (a) 26 100 kg m/s

(b) 34.8 m/s

(c) Yes.

How Science Works ANSWERS

(a) No. The upright position is slightly greater although there is no significant difference between the three sets of readings.

(b) The upright position propels the ball further. This prediction is even stronger if the 2nd go/front measurement is considered to be an anomaly.

(c) No. The measurements have a wide range within each set. There is even overlap of results.

(d) Position of the releae point.(e) Categoric.(f) By measuring the angle of the spoon to the upright.(g) More information can be obtained. A graph can also be drawn and

a pattern discerned (or not).

Documents

AQA GCSE Physics 2-3 Work, Energy & Momentum GCSE Physics pages 146 to 159 July 2010