Intermediate 2 Physics In addition to set homework you will be expected to finish off class notes...

Intermediate 2 PhysicsIn addition to set homework you will be expected tofinish off class notes and regularly review work

againstthe learning outcomes.

You will be expected to take responsibility for your own

learning and for seeking help when you need it. At the

end of each section, you must ensure all notes arecompleted and examples attempted.

In unit 1 we will learn aboutthe physics of motion.

We will focus on the language,principles and laws whichdescribe and explain themotion of an object. Kinematicsis the science of describing themotion of objects using words,diagrams, numbers, graphsand equations.

The goal is to develop mental modelswhich describe and explain the motion ofreal-world objects.

Key words: vectors, scalars, distance,displacement, speed, velocity.

By the end of this lesson you will be able to:

Describe what is meant by vector and scalar quantities

State the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and

directionof the resultant of two forces acting at right angles toeach other.

Scalars and Vectors

Imagine a boatmaking a distresscall to thecoastguard.

The boat tells thecoastguard he is 60 kmfrom Aberdeen.

Scalars and Vectors

Is this enoughinformation for thecoastguard to findthe boat?

Scalars and Vectors

Scalars and Vectors

The coastguard needs both

distance (size)and

direction

to find the boat.

Scalars and Vectors - Definition

A scalar is a quantity which has onlymagnitude (size). It is defined by anumber and a unit.

A vector is a quantity which hasmagnitude (size) and direction. It isdefined by a number, a unit and adirection.

Distance and DisplacementA pupil walks from her house to her school.

Her brother makes the same journey, but via a shop.

How far has the girl walked?

How far has her brother walked?

50 m30 m

40 m

Distance and DisplacementThe girl has walked 50 m.Her brother has walked 70 m.

50 m30 m

40 m

Distance is a scalar quantity – it can be defined simply by a number and unit.

Distance and DisplacementDistance is simply a measure of how much ground an object has covered.

50 m30 m

40 m

Distance and DisplacementBut how far out of place is the girl? And her brother?

Displacement is a vector which requires number, unit and direction.

50 m30 m

40 m

Distance and DisplacementThe girl has a displacement of 50 m at a bearing of 117° East of North.

50 m

30 m

40 m

Distance and DisplacementWhat is her brother’s displacement?

50 m

30 m

40 m

Distance and DisplacementHer brother has a displacement of 50 m at a bearing of 117° (117° East of North).

50 m

30 m

40 m

Distance and DisplacementTheir displacement (how far out of place they each are) is the same.

50 m

30 m

40 m

Speed and Velocity

Speed is a scalar quantity requiring only magnitude (number and unit).

Velocity is a vector, requiring magnitude and direction.

Speed and Velocity

Speed tells us how fast an object is moving.

Velocity tells us the rate at which an object changes position.

Speed and Velocity

Imagine a person stepping one stepforward, then one step back at a speed of0.5 ms-1.

What is the person’s velocity? Remembervelocity keeps track of direction. Thedirection of the velocity is the same asthe direction of displacement.

Speed and Velocity

time

positionin change velocityAverage

time

distancespeed Average

and

Key words: vectors, scalars, distance,displacement, speed, velocity.

By the end of this lesson you will be able to:Describe what is meant by vector and scalar

quantitiesState the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and

directionof the resultant of two forces acting at right angles

toeach other.

Distance and Displacement

Virtual Int 2 Physics – Scalars and Vectors – Distance and Displacement

Speed and Velocity

Virtual Int 2 Physics – Scalars and Vectors – Speed and Velocity

A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity.

The physics teacher walked a distance of 12 meters in 24seconds; thus, her average speed was 0.50 m/s.

However, since her displacement is 0 meters, her averagevelocity is 0 m/s. Remember that the displacement refers tothe change in position and the velocity is based upon thisposition change. In this case of the teacher's motion, there isa position change of 0 meters and thus an average velocity of0 m/s.

Scalar or

Vector?Virtual Int 2 Physics – Scalars & Vectors - Introduction

Key words: vectors, scalars, resultant, scale diagram

By the end of this lesson you will be able to:

Describe what is meant by vector and scalar quantities

State the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and

directionof the resultant of two forces acting at right angles toeach other.

Vectors

Vectors can be represented by a linedrawn in a particular direction.

The length of the line represents themagnitude of the vector.

The direction of the line represents thedirection of the vector.

Addition of Vectors

When two or more scalars are addedtogether, the result is simply a numericalsum.

For example a mass of 3kg and a mass of

5 kg, when added, make a mass of 8kg.

Addition of Vectors

When two or more vectors are addedtogether, providing they act in the

samedirection, the addition is

straightforward.5 N 3 N

8 N

Addition of Vectors

If they are acting in opposite directions

5 N 3 N

2 N

Addition of Vectors

The resultant of two or more vectors

which act at angle to each other can be

found either using a scale diagram, or by

Pythagoras and trigonometry.

To find the resultant of a set of vectors using a scale diagram

1. Decide on a suitable scale and write thisdown at the start

2 Take the direction to the top of the page asNorth. Draw a small compass to show this.

3 Draw the first vector ensuring it is thecorrect length to represent the magnitudeof the vector, and it is the correctdirection.

To find the resultant of a set of vectors using a scale diagram

4. Draw an arrow to represent the secondvector starting at the head of the first.Vectors are always added head to tail.

5 The resultant vector can now be determinedby drawing it on the diagram from the tailof the first to the head of the last vector.The magnitude and direction of this vectoris the required answer.

6 The final answer must have magnitude and direction – either a bearing from North or an angle marked clearly on the diagram

Scale Diagrams

1. Scale: remember if the question is in ms-1 then your scale should be a conversion from cm to ms-1.

2. Direction: draw compass on page

3. 1st vector: length and direction

4. 2nd vector: tail of 2nd starts at tip of first

5. Resultant vector: tail of 1st to tip of last

6. Answer must include magnitude (including units) and direction

Scale Diagrams

Direction should be given as a threefigure bearing from North

e.g. 045° or 175° or 035°

If you give any other angle, you mustclearly mark it on the scale diagram.

A car travels 100 km South, then 140 kmEast. The time taken for the wholejourney is 3 hours.

Using a scale diagram (and the six stepprocess) find(a) the car’s total distance travelled(b) its average speed(c) its overall displacement(d) its average velocity

Scale Diagrams

Scale diagrams are used to find themagnitude and direction of the

resultantof a number of a set of vectors.

Key words: vectors, scalars, resultant, scale diagram

By the end of this lesson you will be able to:

Describe what is meant by vector and scalar quantities

State the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and

directionof the resultant of two forces acting at right angles toeach other.

So you think you know your vectors and scalars?

Mass

Vector definition?

How do you write an answer which is a vector?

Velocity

DistanceKinetic energy

ForceVelocity=

Scale diagram – 6 steps?

Key words: vectors, resultantBy the end of this lesson you will be

ableto:

Use Pythagoras and Trigonometry to find

the magnitude and direction of theresultant of two forces acting at rightangles to each other.

The tropical island of

Sohcahtoa

hypopp

sin

The tropical island of

Sohcahtoa

hypadj

cos

The tropical island of

Sohcahtoa

adjopp

tan

The tropical island of

Sohcahtoa

adjopp

tanhypopp

sinhypadj

cos

hyp

adjcos

hypopp

sin

θ°

adjopp

tan

adj

hyp

opp

The Old Arab Carried A Heavy Sack Of Hay

Tan = Opp/Adj; Cos= Adj/Hyp; Sin=Opp/Hyp

222 oppadjhyp

TheoremPythagoras

'

θ°

adj

hyp

opp

The squaw on the hippopotamus is equal

to the sum of the squaws on the other

two hides

= +

N

E4 km East

+ 3 km North

Remember: The vectors above are not tip to tail. You must join them tip to tail

N

E4 km East

+ 3 km North

R = ?R = ?kmR 534 22

09.364

3tan

1

= Bearing of 053.10

6N North, 8N East - what is the resultant force R ?

6N

8NWe ADD vectors HEAD to TAIL [tip to toe]

RNR 1068 22

333.16

8tan

01.53

6N

Key words: average speed

By the end of this lesson you will be able to:

Describe how to measure an average speed

Carry out calculations involving distance, time

and average speed.

Which of these are units of speed?

miles per hour

gallons

Newtons

seconds

metres

amperesmiles

minutes

metres per second

kilometres per second

wattsmiles per minute

Speeds in….

In Physics we normally use units

m/s for velocity.

Average speed (m/s)

Light speed

Earth in orbit

7500 m/s

High speed train

648 m/s

833 m/s

Falcon

31 m/s

747 jumbo jet

Sound

13.4 m/s

Air molecule

Walking speed

Olympic sprinter

Snail

300000000 m/s

29790 m/s

Earth satellite

60 m/s

Concorde

Fast jet

97 m/s

UK motorway

270 m/s

340 m/s

UK town

500 m/s

1.7 m/s

10.3 m/s

0.006 m/s

Average speed ( m/s )Light speed 300000000 m/s

Earth in orbit 29790 m/s

Earth satellite 7500 m/s

High speed train 60 m/s

Concorde648 m/s

Fast jet833 m/s

Falcon 97 m/s

UK motorway31 m/s

747 jumbo jet270 m/s

Sound 340 m/s

UK town 13.4 m/s

Air molecule500 m/s

Walking speed 1.7 m/s

Olympic sprinter10.3 m/s

Snail 0.006 m/s

What is speed?

When we talk about speed we mean…

the distance covered by an object in agiven time.

What is speed?

If Hamish (the dog) runs 10 metres in 2

seconds, what is his speed?

What is speed?

His speed is 5 metres per second.

So speed is

timedistance

What is speed?

If you forget the formula think of cars travelling at 30 kilometres per hour

timedistancekm

Per

Hour=

Key words: average speed

By the end of this lesson you will be able to:

Describe how to measure an average speed

Carry out calculations involving distance, time

and average speed.

distance

speed time

Speed Calculations

A cyclist travels 100 m in

12 s. What is her speed?

Step 1: write down what you know.

d = 100 m

t = 12 s

s = ?

Step 2: write down your formula. You can use the triangle to help you but remember you get no marks for this!

d = 100 m

t = 12 s

s = ?d = s x t

Step 3: substitute in your values.

d = 100 m

t = 12 s

s = ?

d = s x t

100 = s x 12

Step 4: rearrange

d = 200 m

t = 40 s

v = ?

d = s x t

100 = s x 12

s = 100

12

Step 5: calculate

d = 100 m

t = 12 s

v = ?

d = s x t

100 = s x 12

s = = 8.33100

12

Step 6: units!!!!

d = 100 m

t = 12 s

s = ?

d = s x t

100 = s x 12

s = = 8.33 m/s100

12

Key words: average speed, instantaneousspeed

By the end of this lesson you will be able to:

Describe how to measure instantaneous speed.

Identify situations where average speed andinstantaneous speed are different.

Instantaneous and average speed

Are instantaneous and average speed the same?

Instantaneous or average?

A car’s speed between Arbroath andDundee

Average

Instantaneous or average?

The speed read from a car’s speedometer

Instantaneous

Instantaneous or average?

A tennis ball’s speed as it crosses the net

Instantaneous

Instantaneous or average?

A racing car’s speed over a lap of the track

Average

Instantaneous or average?

A parachutist’s speed as he/she lands

Instantaneous

Key words: acceleration, velocity

By the end of this lesson you will be able to:

Explain the term “acceleration”

State that acceleration is the change invelocity per unit time

Carry out calculations involving the relationshipbetween initial velocity, final velocity, time anduniform acceleration.

Measuring Acceleration Activity 3

Position of light gate from bottom of slope

Acceleration (m/s2)

1st attempt

2nd attempt

3rd attempt

Position 1

m

Position 2 m

Position 3 m

Position 4 m

Average acceleration (m/s2)

What do you expect to happen to the value of acceleration as the light gate is moved further up the slope?

What is acceleration?

Acceleration is the change in velocity of an object per second (in one second).

Is acceleration a vector or scalar quantity?

Acceleration

What is the definition of acceleration?

Is it a vector or a scalar?

Acceleration is the rate of change of velocity per unit time OR change in velocity per unit time.

Vector – since velocity is a vector.

What is acceleration?

The rocket starts off at 0 m/s and 1second later is travelling at 10 m/s. What is its acceleration?

10 metres per second per second 10 m/s2

change in speed in one second

Calculating acceleration

We need to know…the change in velocity so…initial velocity (u)

final velocity (v)and…

time (t)

timevelocity in change

onaccelerati

time(u) velocity initial - (v) velocity final

onaccelerati

tu-v

a

tuv

a

change in velocity

in one second

Acceleration

a = acceleration measured in m/s2

u = initial velocity measured in m/sv = final velocity measured in m/st = time measured in s

Units of acceleration

a = final velocity – initial velocity

time

acceleration is measured in m/s2

If the speed is measured in kilometres per hour, acceleration can be measured in kilometres per hour per second.

Acceleration p4

An object accelerates at a rate of 4 m/s2.

What does this mean?

The object goes 4 m/s faster eachsecond.

Acceleration p4

The object goes 4 m/s faster eachsecond.If the object is initially at rest, whatis its velocity after:1s? 4 m/s2s? 8 m/s3s? 12 m/s4s? 16 m/s

Acceleration

What does it mean if an object has a negative

value of acceleration?

It means that it is slowing down.

For example: an object which has anacceleration of -2 m/s2 is becoming 2 m/sslower each second.

Acceleration Calculations

A car, starting from rest, reaches avelocity of 18 m/s in 4 seconds. Find theacceleration of the car.

What do I know?Initial velocity u = 0 m/sFinal velocity v = 18 m/stime t = 4 s

Acceleration Calculations

What do I know?Initial velocity u = 0 m/sFinal velocity v = 18 m/stime t = 4 s

Formula?

2/5.44

018sm

t

uva

Acceleration Calculations

A cheetah starting from rest acceleratesuniformly and can reach a velocity of 24m/s in 3 seconds. What is theacceleration?

Use technique and show all working!Units!!

Acceleration Calculations

A student on a scooter is travelling at 6 m/s. 4 seconds later, she is travelling at2 m/s. Calculate her acceleration.

Use technique and show all working!Units!!What do you notice about her change invelocity?

Rearranging the acceleration equation

v-u

a t

Rearranging the acceleration equation

v-u

a t a

uvt

atuv

atuv

Key words: acceleration, velocity

By the end of this lesson you will be able to:

Explain the term “acceleration”

State that acceleration is the change invelocity per unit time

Carry out calculations involving the relationshipbetween initial velocity, final velocity, time anduniform acceleration.

Graph results

Acceleration using two light gates

http://www.crocodile-clips.com/absorb/AP5/sample/media/010102AccnApp.swf

The length of the mask is 5 cm. Calculatethe acceleration.

Remember calculate u (initial velocity) andv (final velocity) and use

tu-v

a

Acceleration using a double mask

http://www.crocodile-clips.com/absorb/AP5/sample/media/010102AccnApp2.swf

The length of each section mask is 4 cm. The gap is also 4 cm. Calculate the acceleration.

Remember calculate u (initial velocity) andv (final velocity) and use

tu-v

a

Key words: acceleration, velocity, displacement

By the end of this lesson you will be able to:

Draw velocity-time graphs of more than oneconstant motion.

Describe the motions represented by avelocity-time graph.

Calculate displacement and acceleration, fromvelocity-time graphs, for more than one constantacceleration.

Graphing Motion

Information about the motion of anobject can be obtained from velocity-

timegraphs.

Similarly, we can graph motion based on

descriptions of the motion of an object.

Velocity-time graph

The motion of a moving object can berepresented on a velocity – time graph.

Virtual Int 2 Physics – Mechanics and Heat – Velocity and Acceleration – Velocity Time Graphs

Vectors and Direction

When dealing with vector quantities we

must have both magnitude and

direction.

When dealing with one-dimensionalkinematics (motion in straight lines) weuse + and – to indicate travel in oppositedirections. We use + to indicate accelerationand – to indicate deceleration.

Velocity-Time Graphs

)/( smv

)( st

Constant velocity – does not change with time

00

Describe the motion of this object.

Velocity-Time Graphs

)/( smv

)( st

Increasing with time – constant acceleration

00

Describe the motion of this object.

Velocity-Time Graphs

)/( smv

)( st

Decreases with time – constant deceleration

00

Describe the motion of this object.

Velocity-Time Graphs

)/( smv

)( st0

0

Describe the motion of this object.

Speed-Time Graphs

)/( smspeed

2

00

Calculate the distance covered by the object in the first 10 s of its journey.

10 )( st

The area under the graph tells us the distancetravelled.

Speed-Time Graphs

)/( smspeed

2

00

Calculate the distance covered by the object in the first 10 s of its journey.

10 )( st

The area under the graph tells us the distancetravelled.

Key words: forces, newton balance, weight, mass, gravitational field strength.

By the end of this lesson you will be able to:

Describe the effects of forces in terms of their ability tochange the shape, speed and direction of travel of an object.

Describe the use of a newton balance to measure force.

State that weight is a force and is the Earth’s pull on anobject.

Distinguish between mass and weight.

State that weight per unit mass is called the gravitationalfield strength.

Carry out calculations involving the relationship between weight, mass and

gravitational field strength including situations where g is not equal to 10

N/kg.

What effect can a force have?

Force is simply a push or a pull.

Some forces (e.g. magnetic repulsion, or

attraction of electrically chargedobjects) act at a distance.

What is force?

A force can

change the shape of an objectchange the velocity of an objectchange the direction of travel of an object

Virtual Int 2 Physics – Mechanics & Heat – Forces - Introduction

Units of Force?

Force (F) ismeasured innewtons (N).

Measuring Forces

A Newton (orspring) balance

canbe used to

measureforces.

Mass and Weight

We often use the words mass and weight

as though they mean the same…

but do they?

Mass and Weight

An object’s mass is a measure of how much “stuff” makes

upthat object – how much matter, or howmany particles are in it.

Mass is measured in

grams or kilograms.

Mass and Weight

An object’s weight is the force exerted by gravity on a

mass.

Since it is a force, weight must bemeasured in

newtons.

Investigating the relationship between mass and weight

How can we find the relationship between

mass and weight?

A newton balance can be used to find the

weight of known masses.

Results

Mass Weight in N

100g

200g

300g

400g

500g

1kg

2kg

5kg

Relationship between mass and weight

From this we can see a relationshipbetween mass and weight

100g = 0.1 kg -> 1 N1kg -> 10 N

To convert kg -> N multiply by 10To convert N -> kg divide by 10

Gravitational Field Strength (g)

Gravitational field strength on Earth is

10 N / kg

What is gravitational field strength?

This is the pull of gravity on eachkilogram of mass.

So on Earth, the pull of gravity on a 1kg

mass is 10 N

What is gravitational field strength?

and the pull of gravity on a 2 kg mass is

20 N

Definition

A planet’s gravitationalfield strength is thepull of gravity ona 1 kg mass.

Gravity in the universe

Is gravitational field strength always the

same?

No! It varies on different planets.

http://www.exploratorium.edu/ronh/weight/index.html

Your weight on different planets

Use the website to find your weight ondifferent planets for a mass of 60 kg (aweight of 600 N on Earth).

From this calculate the gravitational field

strength for each planet.

Mass on Earth = 60 kgWeight on Earth = 600 NGravitational field strength =

Weight on Mercury = 226.8 N g = Weight on Venus = 544.2 N g = Weight on the Moon = 99.6 N g = Weight on Mars = 226.2 N g = Weight on Jupiter = 1418.4 N g = Weight on Saturn = 549.6 N g =

1060

600

78.360

8.226

07.960

2.544

77.360

2.226

66.160

6.99

64.2360

4.1418

91.960

6.549

Units for g

We found g by dividing weight in newtons

by mass in kilograms.

What are the units for g?

10 N / kg

Which of the planets has the greatestgravitational field strength?

Why do you think this is the case?

Weight, mass and gravity

We have seen that there is a link between

weight, mass and gravity.

On Earth

1 kg acted on by 10 N / kg weighs 10 N

mass Gravitational field strength g weight

m x g = W

W = mg

Weight, mass and gravity

Weight measured in newtons

Mass measured in kg

Gravitational field strength measured in N / kg

Why is weight measured in newtons?

Key words: friction, forceBy the end of this lesson you will be

ableto:State that the force of friction can opposethe motion of an object.

Describe and explain situations in whichattempts are made to increase or

decreasethe force of friction.

Frictional Forces

Moving vehicles such as cars can slowdown due to forces acting on them.

These forces can be due to…road surface and the tyresthe brakesair resistance.

Virtual Int 2 Physics – Mechanics & Heat – Forces – Friction

Frictional Forces

The force which tries to oppose motion is

called the force of friction.

A frictional force always acts to slow an

object down.

Increasing Friction

In some cases, we want to increasefriction. Some examples of this are:

• Car brakes – we need friction betweenthe brake shoes and the drum to slowthe car down

• Bicycle tyres – we need friction to give• “grip” on the surface

Increasing Friction

On the approach to traffic lights androundabouts, different road surfaces

areused to increase friction compared

withnormal roads.

Decreasing Friction

In some cases, we want to decreasefriction. Some examples of this are:

• Ice skating• Skiing• Aircraft design

Reducing Friction

Friction can be reduced by:

Lubricating the surfaces – this generallymeans using oil between two metalsurfaces. This is done in car engines toreduce wear on the engine – metal partsaren’t in contact because of a thin layerof oil between them.

Reducing Friction

Friction can be reduced by:

Separating surfaces with air (e.g. ahovercraft).

Making surfaces roll (e.g. by using ballbearings).

Reducing Friction

Friction can be reduced by:

Streamlining. Modern cars are designed

to offer as little resistance (or drag) tothe air as possible, reducing friction onthe car.

Streamlining

Cars are streamlined (that is, have their

drag coefficient reduced) by

Reducing the front area of the carHaving a smooth round body shapeUsing aerials built into the car windows

Virtual Int 2 Physics – Mechanics & Heat - Forces – Friction Effects

Key words: force, vector, balancedforces By the end of this lesson you will be ableto:State that force is a vector quantity.State that forces which are equal in size butact in opposite directions on an object arecalled balanced forces and are equivalent tono force at all.Explain the movement of objects in terms ofNewton’s first law.

Force

Force is a vector quantity. What do wemean by this?

To describe it fully we must have size

and direction.

Balanced Forces

Balanced forces are EQUAL FORCES which act in OPPOSITE DIRECTIONS. They CANCEL EACH OTHER OUT.

FF

If balanced forces act on a STATIONARY OBJECT, it REMAINS STATIONARY.

FF

If balanced forces act on a MOVING OBJECT, it continues moving in the same direction with CONSTANT VELOCITY.

F

This is summarised by NEWTON’S FIRST LAW which states:

An object remains at rest, or moves in a straight line with constant velocity unless an UNBALANCED FORCE acts on it.

Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law

To understand NEWTON’S FIRST LAW remember:

An object tends to want to keep doing what it is doing (so if it is sitting still it wants to stay that way, and if it is moving with constant velocity it wants to keep going).

This reluctance to change motion is known as inertia.

The greater the mass, the greater the reluctance.

Think! Is it easier to stop a tennis ball travelling towards you at 10 m/s or to stop a car travelling towards you at 10 m/s?

Forces and Supported Bodies

A stationary mass mhangs from a rope.

What is the weight of

the mass? In whatdirection doesthis act?

W = mg downwards

m

Forces and Supported Bodies

The mass is stationary.Newton’s law tells usthat the forces mustbe

balanced forces.The weight iscounterbalanced by aforce of the same sizeacting upwards due tothe tension in thestring.

m

Forces and Supported Bodies

A book of mass mrests on a shelf.

What is the weight of

the book? In whatdirection doesthis act?

W = mg downwards

m

Forces and Supported Bodies

The mass is stationary.Newton’s law tells usthat the forces must

be

balanced forces.

The weight iscounterbalanced by aforce of the same sizeacting upwards due tothe shelf.

m

What forces are acting on this stationary hovering helicopter?

W = mg

lift =W = mg

Newton’s First Law

Newton’s first law tells us that when theforces on an object are balanced, astationary object will remain stationary.

But it also says that if when forces arebalanced, an object moving at constantvelocity will continue in the same

directionwith the same velocity.Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law

A moving carIf a car moves with constant velocity, then what forces are acting on it?

The ENGINE FORCE and the FRICTION FORCE must be equal.

Engine force

Friction force

Newton’s Law & Car Seat BeltsIf a car stops suddenly, someone inside the car appears to be “thrown forwards”.

In fact, they simply carry on moving with the car’s previous speed.

A seat belt prevents this happening by applying an unbalanced force to the person, in the direction opposite to motion. This causes rapid deceleration.

No seatbelt – what’s going to happen when the car hits the wall?

Explain this in terms of Newton’s 1st law.

What’s going to happen when the motorbike hits the wall?

Explain this in terms of Newton’s 1st law.

Air bagsAir bags produce a similar effect to seatbelts. They apply a force which opposes the motion, causing rapid deceleration.

The large surface area also spreads the force of impact, reducing the pressure and reducing injury.

Terminal velocity

Any free-falling object in a fluid (liquid or gas) reaches a top speed, called ‘terminal velocity’.

Forces in a Fluid

Terminal velocity

The air resistance acting on a moving object increases as it gets faster.

Terminal velocity is reached when the air-resistance (acting upwards) has increased to the same size as the person’s weight (acting downwards)

W = weight

Friction Ff(air resistance) = 0 N

time = 0s, velocity = 0 m/s, friction = 0 N

a = -10 m/s2

W = weight

Ff

a < -10 m/s2

v

W = weight

Ff

a = 0 m/s2

v

Equal & opposite forcesAcceleration zeroTerminal velocity

Velocity – Time Graph

velocity(m/s)

00

time (s)

Terminal velocity

Virtual Int 2 Physics – Mechanics & Heat – Forces - Terminal Velocity

weight

air resistance

Terminal velocity is reached when the air resistance balances the weight.

Terminal Velocity

What effect does opening a parachutehave on the terminal velocity?

When the parachute is opened, air resistanceincreases a lot. There is now an unbalanced forceupwards, which causes deceleration. The velocitydecreases, and the air resistance decreases untilthe forces are balanced again. The parachutistfalls to the ground with a lower terminal velocity.

Virtual Int 2 Physics – Mechanics & Heat – Forces - Terminal Velocity

Key words: Newton’s second law,unbalanced forces, mass, force,accelerationBy the end of this lesson you will be

ableto:Describe the qualitative effects of the change ofmass or of force on the acceleration of an objectDefine the newtonCarry out calculations using the relationshipbetween a, F and m and involving more thanone force but in one dimension only

The example of the parachutist accelerating until the forces are balanced helps us to understand NEWTON’S SECOND LAW which states:

When an object is acted on by a constant UNBALANCED FORCE the body moves with constant acceleration in the direction of the unbalanced force.

Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law

Force, mass and acceleration

F = maForce (N)mass (kg)

Acceleration (m/s2)

Virtual Int 2 Physics – Mechanics & Heat – Forces - Force, mass and acceleration

Force, mass and acceleration

One newton (1N) is the force required to

accelerate 1 kg at 1 m/s2

F = ma

Find the unbalanced force required to accelerate a 4 kg mass at 5 m/s2

What do I know?m = 4kga = 5m/s2

F = maF= 4 x 5F = 20 N

Key words: free body diagrams, resultantforceBy the end of this lesson you will be ableto:Use free body diagrams to analyse the forceson an objectState what is meant by the resultant of anumber of forcesUse a scale diagram, or otherwise, to find themagnitude and direction of the resultant oftwo forces acting at right angles to eachother.

Newton’s First Law

A body remains at rest, or continues atconstant velocity, unless acted upon by

anexternal unbalanced force.

(that is objects have a tendency to keepdoing what they are doing)

Newton’s Second Law

Newton’s Second Law is about thebehaviour of objects when forces are notbalanced.

The acceleration produced in a body isdirectly proportional to the unbalancedforce applied and inversely proportional

tothe mass of the body.

Newton’s Second Law

In practice this means that

the acceleration produced increases asthe unbalanced force increases

the acceleration decreases as the mass of

the body increases

Which forces?

An object may be acted upon by a numberof forces but

only an overall unbalanced forcewill lead to acceleration in the directionof that force.

Forces are measured in…?

Newton’s Second Law can be written as

or more commonly

mF

a

maF

Forces are measured in…?

which gives us the definition of the Newton:

1N is the resultant (or unbalanced) force which causes a mass of 1kg toaccelerate at 1m/ s2

maF

2/11 skgmN

Quick Quiz

Unbalanced force (N)

Mass (kg) Acceleration(m/ s2)

10 2

20 2

20 4

2 5

10 10

5

10

5

10

1

Direction of force

Consider the oil drop trail left by the carin motion.

In which direction is the acceleration?

In which direction is the unbalancedforce?

To the right

To the right

Direction of force

Consider the oil drop trail left by the car

in motion.

In which direction is the unbalancedforce?

To the left – the car is moving to the right and slowing down.

Newton’s First and Second Laws

Remember

Forces do not cause motion

Forces cause acceleration

Free-Body DiagramsA free body diagram is a specialexample of a vector diagram.

They show the relative magnitudeand direction of all forces actingon an object.

They are used to help you identifythe magnitude and direction of anunbalanced Force acting on anobject.

Using Newton’s Second Law

In the simplest case

mFun

mF

a UN

Using Newton’s Second Law

mF1

mFF

a 21

F2

Direction of acceleration?Direction of unbalanced force?Formula for calculating acceleration?

Solving Problems

• Always draw a diagram showing all knownquantities (forces – magnitude anddirection, resultant acceleration anddirection, mass of object(s) )

• Remember that Fun=ma can be applied tothe whole system

• When working in the vertical directionalways include the weight

Key words: acceleration, gravitationalfield strength, projectilesBy the end of this lesson you will be ableto:Explain the equivalence of acceleration due togravity and gravitational field strengthExplain the curved path of a projectile interms of the force of gravityExplain how projectile motion can be treatedas two separate motionsSolve numerical problems using the above

methodfor an object projected horizontally.

Acceleration due to GravityDefinition:

A planet’s gravitational field strength equals the force of gravity PER UNIT MASS.

Units? N/kg

To calculate an object’s weight, use this equation -

mgW Virtual Int 2 Physics – Projectiles – Acceleration due to gravity and gravitational field strength

Near a planet’s surface all objects experience the same gravitational acceleration.

This acceleration is numerically equal to the planet’s gravitational field strength.

ga

Acceleration due to Gravity

For example, on Earth –

g = 10 N/kg

A free-falling object will experience acceleration of a = -10 m/ s2

What does the –ve sign tell you?

Acceleration due to Gravity

Gravitational field strength

Is the gravitational field strength the same on eachplanet?

How does distance affect gravitational field strength?

It decreases the further away you are from the planet’ssurface.

What will happen to the weight of an object as it getsfurther from the surface? Explain your answer.

It will decrease.

The force of gravity nearthe Earth’s surface givesall objects the sameacceleration.

So why doesn’t thefeather reach the

groundat the same time as theelephant?

Why are the gapsbetween the ballsincreasing?

An object is released from rest close to the Earth’ssurface. Which formula can be used to find its velocityat a given time?

v = u + atwhere v = ? , u = 0 , a = , t =

What is its velocity:At the time of release?After 1 second?After 2 seconds?After 3 seconds?After 4 seconds?

Projectiles

Virtual Int 2 Physics – Projectiles –Projectile Motion

Forces acting on projectiles

What would happen to a ball kicked off a

cliff, in the absence of gravity?

Forces acting on projectilesThere would be no vertical motiontherefore the ball would continue atconstant speed in a straightline (remember Newton’s first law)

What is the initial vertical speed of aprojectile fired horizontally?

How will the horizontal speed vary during

the object’s flight?

0 m/s

It will remain the same as the initial horizontal speed.

Objects projected horizontallyThink about…

Describe the vertical motion of an object

projected horizontally:It will accelerate downwards due to gravity.

Objects projected horizontallyThink about…

Projectiles

Virtual Int 2 Physics – Projectiles –Comparing Projectile Motion with Vertical Motion

Virtual Int 2 Physics – Projectiles – Graphs of Projectile Motion

What formula can be used to find thehorizontal displacement of an objectfired horizontally if horizontal velocityand time of flight are known?

sh = vht

Objects projected horizontallyThink about…

horizontal displacement (m)

horizontal velocity (m/s)

time of flight (s)

http://www.fearofphysics.com/XYIndep/xyindep_correct.html

Which ball will hit the ground first?

SummaryHorizontal motion

Vertical motion

ForcesAre there forcespresent? If so, inwhat direction arethey acting?

No Yes

The force of gravityacts downward

AccelerationIs there acceleration?If so, in whatdirection? What isthe value of theacceleration?

No Yes

Acceleration = "g" downwardat 10 m/s2

VelocityConstant or changing?

Constant Changing

by 10 m/s each second

Solving Numerical Problems

• Always write down what you know – many questions have a lot of text surrounding the Physics so pick out the information from the question

• Write down other relevant information you have e.g. acceleration due to gravity

• Select formula – this isn’t a test of memory so while you should learn your formulae, don’t be afraid to check against the data book or text book

• Substitute values and rearrange formula• Write answer clearly remembering magnitude

and direction, and units.

Example

A flare is fired horizontally out to sea from acliff top, at a horizontal speed of 40 m/s. Theflare takes 4 s to reach the sea.

(a) What is the horizontal speed of the flare after 4 s?

There are no forces acting in the horizontal. The

horizontal speed remains the same = 40 m/s.

Example

(b) Calculate the vertical speed of the flare after 4s

final speed v = ?initial vertical speed u = 0 m/s Initial vertical speed is always 0 m/s!

acceleration a = 10 m/s2

time t = 4 s

v = u + atv = 0 + 10 x 4v = 40 m/s

Example

(c) Draw a graph to show how vertical speed varies with time.

Initial vertical speed = 0 m/sFinal vertical speed = 40 m/s

Variation of vertical speed with time

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5

Time (s)

Ve

rtic

al s

pe

ed

(m

/s)

Example

(d) Use this graph to calculate the height of the cliff.

Variation of vertical speed with time

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5

Time (s)

Ve

rtic

al s

pe

ed

(m

/s)

Displacement = area under velocity-time graph

½ bh = ½ x 4 x 40= 80 m

Height of cliff = 80 m

Projectiles

Virtual Int 2 Physics – Projectiles Example Problem

Virtual Int 2 Physics – Projectiles –Newton’s Thought Experiment

Key words: Newton’s third law, newtonpairsBy the end of this lesson you will be ableto:State Newton’s third lawIdentify “Newton pairs” in situations involvingseveral forcesState that momentum is the product of massand velocity.State that momentum is a vector quantity.

Forces acting between objects

Newton realised that

When a body is acted upon by a force there must be another body which also has a force acting on it. The forces are equal in size but act in opposite directions.

Newton’s Third Law

If object A exerts a force on object B, then B exerts an

equal and opposite force on A

Forces always occur in equal and opposite pairs

For every action there is an equal and opposite reaction

Force of GUN on BULLET

Firing a gun

Force of BULLET on GUN

Force of RUNNER on

BLOCKS

Starting a sprint

Force of BLOCKS on

RUNNER

Force of EARTH on

APPLE

A falling apple

Force of APPLE on

EARTH

A Rocket

Force of ROCKET on

GAS

Force of GAS on ROCKET

Key words: momentum, law ofconservation of momentumBy the end of this lesson you will be ableto:State that momentum is the product of massand velocity.State that momentum is a vector quantity.State that the law of conservation of linearmomentum can be applied to the interactionof two objects moving in one direction, in theabsence of net external forces.Carry out calculations concerned withcollisions in which all the objects move in thesame direction and with one object initially atrest.

Collisions

When two objects collide, they applyforces to each other.

What does the size of the force dependon?

Virtual Int 2 Physics – Mechanics and Heat – Momentum – Momentum defined

Momentum

The momentum of an object is the

mass x velocity

It is a vector quantity.

It has units of kg m/s

Momentum & CollisionsVirtual Int 2 Physics – Mechanics and Heat – Momentum – Collisions

We will consider two types of collision:

1.Vehicles bounce apart after collision

2.Vehicles stick togetherafter collision

A 2kg trolley travelling at 3 m/s hits astationary 1kg trolley.

After the collision the 2kg trolleycontinues to travel in the same directionat 1 m/s. The 1 kg trolley moves offSeparately. Calculate the velocity of the 1kgtrolley after the collision.

Collisions Examples

How can we find the answer?

Using the Law of Conservation of Momentum!

total momentum before collision =

total momentum after collision

providing no external forces are acting.

A 2kg trolley travelling at 3 m/s hits astationary 1kg trolley.

After the collision the 2kg trolleycontinues to travel in the same directionat 1 m/s. The 1 kg trolley moves offseparately. Calculate the velocity of the 1kgtrolley after the collision.

Collisions Examples

Collisions where vehicles bounce apart

Before After

2 kg

3 m/s

1 kg

0 m/s

2 kg

1 m/s

1 kg

? m/s

m/skg 6

0) x 1 ( 3) x (2

umum before momentum total

2211

momentum = mass x velocity

m/skg 6

) x v1 ( 1) x (2

vmvm after momentum total

2

2211

momentum = mass x velocity

Conservation of momentum tells us momentum before = momentum after

Collisions where vehicles bounce apart

2 kg

1 m/s

1 kg

? m/s

positive) (sinceright the to travelofDirection

/4v

2-6 2-v2

6 v 2

m/skg 6 ) x v1 ( 1) x (2

vmvm after momentum total

2

2

2

2

2211

sm

momentum = mass x velocity

Collisions where vehicles bounce apart

m/skg 6

0) x 1 ( 3) x (2

umum before momentum total

2211

2 kg

1 m/s

1 kg

? m/s

Check does this work?

Conservation of momentum tells us momentum before = momentum after

m/skg 6

4) x 1 ( 1) x (2

vmvm after momentum total

2211

A 1kg trolley travelling at 2 m/s hits astationary 1kg trolley.

After the collision the trolleys stick togetherand continue to travel in the same direction.Calculate the velocity of the combined

vehicleafter the collision.

Collisions Examples

Collisions where vehicles stick together

Before After

1 kg

2 m/s

1 kg

0 m/s

1 kg

? m/s

1 kg

m/skg 2

0) x 1 ( 2) x (1

umum before momentum total

2211

momentum = mass x velocity

m/skg 2

2v

v v

x v)1 ( ) x v(1

v vther,stuck toge are vehiclesSince

) x v1 ( ) x v(1

vmvm after momentum total

21

21

2211

momentum = mass x velocity

Conservation of momentum tells us momentum before = momentum after

Collisions where vehicles stick together

1 kg

? m/s

1 kg

positive sinceright the to travelofDirection

m/s 1v

2 2v

m/skg 2

2v

v v

x v)1 ( ) x v(1

v vther,stuck toge are vehiclesSince

) x v1 ( ) x v(1

vmvm after momentum total

21

21

2211

momentum = mass x velocity

Check does this work?

Conservation of momentum tells us momentum before = momentum after

Collisions where vehicles stick together

1 kg

1 m/s

1 kg

momentum = mass x velocity

m/skg 2

0) x 1 ( 2) x (1

umum before momentum total

2211

m/s2kg

11

1) x 1 ( 1) x (1

/1 v vther,stuck toge are vehiclesSince

) x v1 ( ) x v(1

vmvm after momentum total

21

21

2211

sm

Key words: work done, energy, force,distance, power, timeBy the end of this lesson you will be ableto:State that work done is a measure of theenergy transferred.Carry out calculations involving therelationship between work done, force anddistance.Carry out calculations involving therelationship between work done, power andtime.

Work done?

What is meant by work done in Physics?

When a force acts upon an object tocause a displacement of the object, it

issaid that work was done upon the

object.

Work done?

There are three key ingredients to work –force, displacement, and cause.

In order for a force to qualify as having donework on an object, there must be adisplacement and the force must cause thedisplacement.

Work done?Formula linking work done, force and displacement?

Examples of work done?a horse pulling a plow through the fielda shopper pushing a grocery cart down the aisle of a supermarketa pupil lifting a backpack full of books upon her shouldera weightlifter lifting a barbell above his headan Olympian launching the shot-put, etc.

In each case described here there is a force exerted upon anobject to cause that object to be displaced.

FdEw

Work done

A dog pulls a 4 kg sledge for a distance on

15 m using a force of 30 N. How muchwork does he do?

What do I know?F = 30Nd = 15m

Work doneWhat do I know?F = 30Nd = 15m

Formula?

JE

xE

FdE

w

w

w

450

1530

Virtual Int 2 Physics – Mechanics & Heat – Work Done – Example Problem

Power

Power is the rate of doing work i.e. ifwork is done then the work done persecond is the power.

tE

P Power in watts (joules per seconds)

Energy in joules

time in seconds

Power

A dog pulls a 4 kg sledge for a distance on

15 m using a force of 30 N in 20 s.Calculate the power of the dog.

What do I know?F = 30Nd = 15mt = 20s

PowerWhat do I know?F = 30Nd = 15mt = 20s

Formula?

JE

xE

FdE

w

w

w

450

1530

PowerWhat do I know?F = 30Nd = 15mt = 20sEw = 450J

Formula?

WP

P

tE

P W

52220

450

.

Key words: gravitational potential energy,mass, gravitational field strength, kineticenergy

By the end of this lesson you will be ableto:Carry out calculations involving the relationshipbetween change in gravitational potential

energy,mass, gravitational field strength and change inheight.Carry out calculations involving the relationshipbetween kinetic energy, mass and velocity.

Gravitational Potential Energy

…is the potential energygained by an object whenwe do work to lift itvertically in a gravitationalfield.

Gravitational Potential Energy

The work done in lifting anobject vertically

FdEw What force is required?

Gravitational Potential Energy

FdEw

To lift the object we must overcome the weight W=mg

Gravitational Potential Energy

mgdE

Vertical distance – we call this height h

Gravitational Potential Energy

Virtual Int 2 Physics – Mechanics & Heat – Potential Energy – Example Problem

mghEP

Kinetic Energy

…is the energy associated with a moving object.

Kinetic Energy

depends on…

The mass of the object

depends on…

The velocity of the object

Kinetic Energy

Kinetic Energy

2

2

1mvEK

Virtual Int 2 Physics – Mechanics & Heat – Kinetic Energy – Example Problem

Virtual Int 2 Physics – Mechanics & Heat – Power – Example Problem

Speed and Stopping Distance

The distance required to stop a moving vehicle is a combination of two things:

Thinking distanceBraking distance

Speed and Stopping Distance

Each driver has a reaction time.

The thinkingdistance is thedistance you travelbetween realising youneed to stop andreacting.Thinking distance = speed x reaction time

Speed and Stopping Distance

Braking distance This is the distance you travel between pressing your brakes and the car coming to a stop.

To stop a vehicle, brakes do work to transform Ek into heat. This work = braking force x braking distance.

Speed and Stopping Distance

To stop a vehicle, brakes do work to transform Ek intoheat. This work = braking force x braking distanceEk = Ew = Fd

The kinetic energy depends on the mass and the squareof velocity of the object so as speed increases kineticenergy increases and therefore braking distanceincreases.

Speed and Stopping Distance

Thinking distance = speed x reaction timeBraking distance = speed x braking time

Total stopping distance = thinking distance +braking distance

Look at the graph of velocity against timefrom the moment the driver first sees ahazard until the moment the car comes torest.

velocity(m/s)

00

time (s)0.6 3

16

velocity(m/s)

00

time (s)0.6 3

16

Here, the driver has noticed the hazard but has not yet reacted. The distance travelled is reaction time x speed.

The reaction time is 0.6 s

Why is the graph in two distinct sections?

velocity(m/s)

00

time (s)0.6 3

16

Here, the driver is braking to astop. The braking distance is thedistance travelled while applyingthe brakes.

Why is the graph in two distinct sections?

Use the graph to

- calculate the thinking distance - calculate the car’s braking distance- calculate the car’s overall stopping

distance.

How is stopping distance affected by speed?

Stopping distances

050

100150200250300350400450500

0 50 100 150 200 250

Speed in km per hour

Dis

tanc

e in

met

res

Stoppingdistance

Brakingdistance

Thinkingdistance

Stopping distances

050

100150200250300350400450500

0 50 100 150 200 250

Speed in km per hour

Dis

tanc

e in

met

res

Stoppingdistance

Brakingdistance

Thinkingdistance

Kinetic energy is linked to the square of the velocity

Key words: gravitational potential energy,mass, gravitational field strength, kineticenergy, mass, velocity, input and outputenergy and power, efficiency

By the end of this lesson you will be able

to:Carry out calculations involving therelationship between efficiency and outputpower, output energy and input power,

inputenergy.

Energy Transformations & Efficiency

There are many occasions where energy is

transformed from one form to another.

For example: an electric motortransforms electrical energy in kineticenergy; a light bulb transforms electricalenergy into light energy.

Energy Transformations & Efficiency

However, in these examples, not all theelectrical energy is converted into theuseful form we want!

Some energy may be transformed intoheat, due to friction, and sound. Energy is notlost (the law of conservation of energy) howeverit has been “wasted” because it is not in a usefulform.

Energy Transformations & Efficiency

The efficiency of a machine (or energyconverter) is measured byexpressing the useful energy output as

apercentage of total energyinput.

Energy Transformations & Efficiency

1

100x

input energy totaloutput energy useful

efficiency %

Power & Efficiency

1

100x

input poweroutput power

efficiency %

Virtual Int 2 Physics – Mechanics & Heat – Work, Energy & Power - Efficiency – Example Problem

Conservation of Energy

Energy can neither be created nordestroyed – simply transformed from

oneform into another.