L1 – 2.3 Force & Shape p22 LOs Describe how to measure the extension of an object when it is...

L1 – 2.3 Force & Shape p22

LOs• Describe how to measure the extension of an object

when it is stretched.• Recognise that an elastic body regains its shape after

being deformed.• Describe extension–load graphs for a spring, for rubber

and for polythene.• Interpret extension–load graphs including the limit of

proportionality.• State and use Hooke’s law.

© Boardworks Ltd 20041 of 202 of 37

What are compression and tension?

Compression is the force on a material when

it is being squashed.

Tension is the force on a material when

it is being stretched.


Compression or tension?


The plank bends because there are several forces, including gravity, acting on it.

These forces cause the plank to be squashed one side and stretched on the other.2

Where on the plank do these forces produce compression?

Where on the plank do these forces produce tension?

Standing on a plank

compression

tension


Apply a force to a spring and it changes shape.

Release the force and the spring returns to its original shape.

Materials that behave like this are called elastic.

Can you name another elastic material that will return to its original shape?

sponge

What is an elastic material?


Apply a force to Plasticine and it changes shape.

Release the force and the clay keeps its new shape. It does not return to its original shape.

Materials that behave like this are called plastic.

Can you name another plastic material that will not return to its original shape?

What is a plastic material?

clay


Elastic or plastic?

Springs

The behaviour of springs is important since they have many uses, from car and bike suspension to clock-making.

It is important to know how springs will react when forces are applied.

Applying forces to springs


1. Attach a spring to a stand.2. Record the length of the spring.3. Add a 50g* mass to the spring.4. Record the new length of the spring. 5. Continue to add masses up to 500g in total

and record the length of the spring.

How could you investigate what will happen to a spring as masses are attached to it?

Mass (g)

Load(N)

Length(cm)

Total extension(cm)

0 0 0

50 0.5

Stretching a spring

6. Plot a graph of load against extension.7. What do the results tell you?

* You may need to use small masses dependent on your spring – test it first.


Load (N)

Extension (cm)

Where is the extension proportional to the load?

Extension is proportional to load where the graph is a straight line.

elastic limit

plastic region

What is the name of the point after which the spring will not return to its original shape?

Graph to show load and extension for a spring

Notes:• If an object regains its shape after being stretched or

squashed it is said to be ELASTIC.

• When we stretch an elastic object, its extension is proportional to the force applied.

• It’s important to measure the extension of an object from its resting length.

• If an object does not return to its initial length, it has reached its ELASTIC LIMIT – it has been permanently extended.

Hooke’s law and the force constant (notes)

Hooke’s law states that the extension of a spring, x, is directly proportional to the weight it supports, F.

F µ x or F = kx where k is a constant.

k is called the spring constant. The units of k are Nm-1.

xoriginal length

F

Extension of different materials (notes)

• Springs obey Hooke’s law (until we deform them)

• This is shown by a straight line graph.

• The gradient is k, the spring constant.

Force /N

Ext

ensi

on /c

m

Extension of different materials (notes)

• Hooke’s law only applies up to a point.

• This is the LIMIT OF PROPORTIONALITY.

• Rubber and polythene have lower limits of proportionality than a steel spring.

Prep

• Draw graph of your results and comment on it.

• Complete past paper questions 3 and 2.

L2 – 2.4 Force & Motion 1/2 p24

LOs• Describe how a force may change the motion of an

object.• Recognise that a resultant force acts on an object when

the object accelerates or decelerates.• Recall and use the equation:

‘force = mass × acceleration’


Introducing balanced forces


What is Newton’s first law? (notes)

If the forces on an object are balanced, the object will continue to do what it is already doing:

if the object is stationary, it will remain stationary

if the object is moving, it will continue to move at the same speed and in the same direction.

If the resultant force acting on an object is zero, all the forces are said to be balanced.

This forms the basis of Newton’s first law of motion, which states:


Terminal velocity of a skydiver

Velocity–time graph of skydiver


Introducing unbalanced forces


If the resultant force acting on an object is not zero, all the forces are said to be unbalanced.

This forms the basis of Newton’s second law of motion, which states:

What is Newton’s second law? (notes)

If the forces on an object are unbalanced, two things about the object can change:

the speed of the object may change – it may either increase or decrease

the direction of motion may change.


How is movement calculated from force? (notes)

The resultant force acting on an object is related to the object’s mass and acceleration. These three factors are linked by the following equation:

Resultant force is measured in newtons (N).

Mass is measured in kilograms (kg).

Acceleration is measured in metres per second per second (m/s2).

force = mass x acceleration

F = ma


How do we use Newton’s second law?

A car has a mass of 1,000 kg. What force must the car’s engine supply to cause an acceleration of 2 m/s2?


= 1,000 x 2

= 2,000 N

Using a formula triangle

A formula triangle helps you to rearrange a formula. The formula triangle for force (f), mass (m) and acceleration (a) is shown below.

x

Cover the quantity that you are trying to work out, which gives the rearranged formula needed for the calculation.

So to find force (f), cover up f…

…which gives the formula…

f = m x a


How do we use Newton’s second law?

A lorry has a mass of 12,000 kg. What acceleration is caused by a force of 10,000 N?


= 0.83 m/s2

= 10,000

12,000

forcemass

acceleration =


Using F=ma we can calculate the

acceleration of the trolley.

It won’t accelerate as much as we’d

expect due to friction.

We can reduce the friction by

using a lubricant.

Demo


F = ma calculations

Prep

• F=ma calculation sheet 3• Past paper question 1

Extension• Past paper question 2

L3 – 2.5 Force & Motion 2/2 p26

LOs• Recognise how to find the resultant of two forces that act

along the same straight line.• Describe how to represent a force as a vector.• Recognise that an object in circular motion is acted on

by a centripetal force that acts towards the centre of the circle.


What forces are acting between Mel’s computer and the table it is resting on?

The computer pushes down on the table because it is attracted by the Earth’s gravity.

What forces support objects?

contact force

reactionforce

The table exerts an equal and opposite force pushing upwards on the computer. This is called a reaction force.


A force cannot exist on its own – there is always a second force present.

This forms the basis of Newton’s third law of motion states, which states:

What is Newton’s third law?

These pairs of forces that act between two objects are sometimes called action–reaction pairs.

If object A exerts a force on object B, then object B exerts an equal but opposite force on object A.

Action–reaction pairs


How many pairs of balanced, unbalanced and action–reaction forces can you spot?

Balanced and unbalanced forces


500 N500 N

Think of a car traveling at a constant 50 mph. The engine provides sufficient force to just overcome all the frictional forces that are acting to decrease the speed.

50 mph


50 mph

Cross wind

Now a cross-wind acting on the car produces a sideways force.

This causes the direction of the car to change. This happens because the sideways forces on the car are not balanced.

If the car turns left so that the wind is now BEHIND the car, what will happen to the speed?


The air resistance will decrease because the car has a “tail wind” (it is being blown from behind).

This means the forces acting on the car are no longer balanced. The car will increase in speed (accelerate) until the forces are balanced again.

500 N400 N

> 50 mph

500 N500 N

60 mph


Summary (notes)

If the forces on an object are balanced :

• If it is stopped it will remain stopped.

• If it is moving then it will continue to move at the same speed.

In other words, it will continue to do what it is already doing without any change.

If the forces are unbalanced two things can happen

• The speed will change.

• The direction of motion will change.

This is called acceleration.


Resultant Forces (notes)

The sum effect of more than one force is called the resultant force.

You can find out the resultant force by calculating the difference between opposing forces.

500 N400 N

100 N

A resultant force of 100 N is accelerating the car.


5N5N

20N

1.

Find the resultant force:

10N

Click for solution

Resultant force = 20N -10N = 10N downThe block will accelerate down.


2.5N

5N

5N

5N

Click for solution

Resultant force = 5N - 0N = 5N right.

The vertical forces are equal in size and opposite in direction so there is no resultant force in the vertical direction. The block will accelerate to the right.


13N

3.

10N

20N

10N

3N7N

17N

Click for solution

Resultant force = 30 - 13 = 17N right.

The vertical forces are equal in size and opposite in direction so there is no resultant force in the vertical direction. The block will accelerate to the right.


Centripetal force


Forces and acceleration … reminder

This will cause an acceleration in the direction of the stronger force. This can make an object slow down or speed up, or it can cause it to change direction.

An object will remain stationary or will move in the same direction at a constant speed, unless the forces acting on it are not balanced.


Acceleration in a circle

A motorbike drives round a corner at a constant speed. Its direction changes as it goes round the corner, so even though its speed is constant, it must be accelerating.

This acceleration must be at right angles (perpendicular) to the direction of movement as it turns the corner, otherwise its speed could not be constant.

Which way do you think the motorbike is accelerating, towards the inside of the bend, or away from it?


Force and acceleration are both vector quantities, unlike mass, so according to this equation, their directions must be equal.

Forces causing circular motion

m × aF =

Any object that moves in a circle must be accelerating towards the centre of that circle. What causes this?

What equation do you know that links force and acceleration?

All circular motion must therefore be caused by a force acting towards the centre of the circle.

This type of force is known as a centripetal force.

Thinking about circular motion

A washing machine dries clothes by spinning them round very fast:

It is important to think of circular motion as an object being continuously prevented from moving in a straight line, rather than as if the object is being flung outwards from the centre.

The sides of the drum provide the centripetal force that keeps the clothes moving in a circle, but water is free to escape in straight trajectories through the holes in the sides.


Examples of centripetal forces

Here are two more examples of circular motion caused by centripetal forces:

Can you work out the direction of the force in each case, and describe the type of force involved?

Factors affecting centripetal forces


Understanding centripetal forces

TFFTTT


Centripetal force (notes)

Centripetal force makes an object be continuously prevented from moving in a straight line.

A satellite orbiting a planet is held in orbitby centripetal force acting towards theplanet. In this case, the force is theplanet’s gravity.

The satellite is constantly changing direction, therefore its velocity must be changing. It is ALWAYS ACCELERATING (even though it’s speed remains the same!)

Prep

• Complete AQA Resultant forces activity sheet

• Complete Resultant forces PPQ

L4 – 3.1 Moments p30

LOs• Describe what is meant by the moment of a force about

a point.• Recognise and describe everyday examples of

moments.• Describe the balancing of a beam about a pivot.


5N

A force acting on an object can cause it to turn about a pivot.

pivot

Force and rotation (notes)

What happens to the see-saw when a force is applied on the left-hand side?

Does the seesaw turn? If so, clockwise or anti-clockwise?


pivot

The left-hand side of the see-saw moves downwards when a force is applied to it – this is an anticlockwise turn.

The turning effect of a force is called a moment.

Force and rotation – a moment (notes)


A spanner is a lever that can be used to unscrew a nut.

force

pivot

distance from force

to pivot

Using moments

If the moment is big enough it will unscrew the nut.

If not, there are two ways of increasing the moment.

The spanner exerts a moment or turning force on the nut.


1. Increase the distance from the force to the pivot – apply the force at the end or use a longer spanner.

Using moments – increasing the moment

force

If the same force is applied over a greater distance, a larger moment is produced.

pivot

distance from force

to pivot


2. Increase the force applied – push/pull harder or get someone stronger to do it!

Using moments – increasing the moment

force

If a greater force is applied over the same distance, a larger moment is produced.

pivot

distance from force

to pivot


How to increase the moment ….

If the same force is applied over a greater distance, a larger moment (turning force) is produced.

If a greater force is applied over the same distance, a larger moment is produced.

Using moments – increasing the moment (notes)


moment = force (N) x distance from pivot (cm or m)

The turning effect of a force is called a moment.

The moment of a force is given by the equation:

Moments are measured in Newton centimetres (Ncm) or Newton metres (Nm).

moment

f x d

Moment equation (notes)


Gina weighs 500 N and stands on one end of a seesaw. She is 0.5 m from the pivot.

What moment does she exert?

moment = 500 x 0.5

= 250 Nm

0.5 m

500 N pivot

Moment calculation


Set up this apparatus.

Investigate changing the distancesbetween pivot and newton meter.

Investigate changing the distances between pivot and mass.

Investigate changing the mass.

What do you notice?

Moments investigation

weight (N) x distance (m) = Moment

x =

x =

x =

x =

x =

x =

Prep

• Write up the Moments practical.• Complete “How Levers Work” sheet.

L5 – 3.2 Moments in Balance p22

LOs• Recognise that there is no resultant force or resultant

turning effect on an object in equilibrium.• Use knowledge of forces and turning effects to explain

why objects at rest don’t move or turn.

• Still to be written

Prep

• Moments equilibrium PPQ (2 mins).• Worksheet 6 Law of moments• PPQ 2 Moments in balance

L6 – 3.3 Principle of moments p34

LOs• Use knowledge of turning effects to explain why a

pivoted object is in equilibrium.• Describe the Principle of Moments.• Apply the principle of moments to simple systems in

equilibrium.

• What’s my mass? Or what’s your mass?

MEMasses

Principle of moments

The girl on the right exerts a clockwise moment, which equals...

The girl on the left exerts an anti-clockwise moment,which equals...

her weight x her distance from pivot

her weight x her distance from pivot

pivot

Principle of moments (notes)

When something is balanced about a pivot:

total clockwise moment = total anticlockwise momentW1d1 = W2d2

If the anticlockwise moment and clockwise moment are equal then the see-saw is balanced. This is known as the principle of moments.

pivot


The principle of moments can be investigated using 10g masses with a balance.

moment (left) = 10 x 7 = 70 gcm

moment (right) = (10 x 3) + (10 x 4)

= 70 gcmW1d1 = W2d2 + W3d3

Both moments are equal and so the see-saw is balanced.

Principle of moments (notes)


Two girls are sitting on opposite sides of on a see-saw. One girl weighs 200 N and is 1.5 m from the pivot. Where must her 150 N friend sit if the seesaw is to balance?

When the see-saw is balanced:

Principle of moments – calculation

total clockwise moment = total anticlockwise moment

200 N x 1.5 m = 150 N x distance

200 x 1.5 = distance150

distance of second girl = 2 m

Tower cranes are essential at any major construction site.

load armtrolley

loading platform

tower

Concrete counterweights are fitted to the crane’s short arm. Why are these needed for lifting heavy loads?

counterweight

Why don’t cranes fall over?

Using the principle of moments, when is the crane balanced?

moment of = moment of load counterweight

If a 10,000 N counterweight is three metres from the tower, what weight can be lifted when the loading platform is six metres from the tower?

6 m

3 m

10,000 N?


moment of counterweight

distance of counterweight from tower

=

= 10,000 x 3= 30,000 Nm

counterweight x

moment of load

=

= ? x 6

load x distance of load from tower

moment of load = moment of counterweight ? x 6 = 30,000

? = 3,000 6

? = 5,000 N


At what distance can the loading platform carry each load safely?

Crane operator activity

Prep

• Principle of moments PPQ 3• Construct a mobile consisting of at least 3

elements of different mass such that each beam is precisely horizontal. This one is made from drinking straws and paperclips

After half term …

• We’ve one more lesson and then a test. You may wish to look over forces and moments over the holiday…..

Glossary

counterbalance – A weight used to balance another weight.effort – The force applied to use a lever.

lever – A simple machine that moves about a pivot and makes work easier by increasing the size of a force.

load – The force moved when using a lever.moment – The turning effect of a force. It equals the force

multiplied by the distance from the pivot.

pivot – The point around which a lever turns.

L1 – 2.3 Force & Shape p22 LOs Describe how to measure the extension of an object when it is...

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