Forces

Part ofPhysicsMotion, forces and energy

Change of shape

When a acts on an object, the object may change shape by bending, stretching or compressing - or a combination of all three shape changes. However, there must be more than one force acting to change the shape of a stationary object in the following ways:

A beam is bent.Two equal forces act inwards to support left hand end. A third force bends the right had end downwards.

Pull an object's ends apart, eg when a rubber band is stretched.

A beam is stretched by two equal forces. Beam is thinner in the middle to indicate stretching. Arrows at each end indicate direction of force.

Push an object's ends together, eg when an empty drink can is squashed.

A beam is squashed by two equal forces. Beam is thicker in the middle to indicate compression. Arrows either end point inwards to indicate direction of force.

Bend an object's ends past each other, eg when an archer pulls an arrow back against a bow.

A change in shape is called :

  • deformation is reversed when the force is removed - there is no permanent change in shape.

  • inelastic deformation is not fully reversed when the force is removed - there is a permanent change in shape.

A rubber band undergoes elastic deformation when stretched a little. A metal drink can undergoes inelastic deformation when it is squashed.

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The force-extension graph

force extension graph

A force-extension graph can be used to calculate the work done in joules when stretching a spring.

In a force-extension graph:

  • the gradient is the spring constant

  • the area under the line is the work done in stretching the spring

force extension graph

Practical experiment- how forces affect the extension of a spring

There are different ways to investigate the relationship between force and extension on a spring. In this practical activity it is important to:

  • measure and record length accurately

  • measure and observe the effect of force on the extension of springs

  • collect the data required to plot a force-extension graph

Aim of the experiment

To investigate the relationship between force and extension on a spring.

Method

A clamp stand holds both a spring and a ruler. The spring has a weight hooked onto the bottom. The clamp is attached to a bench.
  1. Secure a clamp stand to the bench using a G-clamp or a large mass on the base.

  2. Use bosses to attach two clamps to the clamp stand.

  3. Attach the spring to the top clamp, and a ruler to the bottom clamp.

  4. Adjust the ruler so that it is vertical, and with its zero level with the top of the spring.

  5. Measure and record the unloaded length of the spring. Remember to measure to the same point each time.

  6. Hang a 100 g slotted mass carrier - weight 0.98 newtons (N) - from the spring. Measure and record the new length of the spring. Add a 100 g slotted mass to the carrier. Measure and record the new length of the spring.

To convert mass in grams to weight in newtons (\(N\)), you can use the formula \(W\) \(=\) \(mg\), where \(W\) is the weight in newtons, \(m\) is the mass in kilograms, and \(g\) is the gravitational field strength in newtons per kilogram.

Repeat step 6 until you have added a total of 1,000 g.

Results

Record your results in a suitable table.

Force (N)Length (mm)Extension (mm)
0 (unloaded)220
0.985230
1.968361

Analysis

Force extension graph. The line starts from the bottom right corner and slopes upwards with a sharp curve at the end. Axis labelled force and extsnion.
  1. For each result, calculate the extension: extension = length - unloaded length

  2. Plot a line graph with extension on the vertical axis, and force on the horizontal axis. Draw a suitable line or curve of best fit.

  3. Identify the range of force over which the extension of the spring is directly proportional to the weight hanging from it.

Evaluation

It is important to keep the ruler vertical. Suggest another way to improve the accuracy of the length measurements.

Hazards and control measures

HazardConsequenceControl measures
Equipment falling off tableHeavy objects falling on feet - bruise/fractureUse a G-clamp to secure the stand.
Sharp end of the spring recoiling if the spring breaksDamage to eyes, cuts to skinWear eye protection. Support and gently lower masses whilst loading the spring.
Masses falling to floor if the spring failsHeavy objects falling on feet - bruise/fractureGently lower load onto spring and step back.

Extended syllabus content: Limit of proportionality

If you are studying the Extended syllabus, you will also need to know about the term 'limit of proportionality' and to recall and use the spring constant as force per unit extension equation . Click 'show more' for this content:

Activity: Spring extension

This activity demonstrates what happens to springs when you add different weights, or change the strength of the spring.

Video: Hooke's Law

In this short video Professor Brian Cox highlights the effect of forces in changing the shape of an object. Hooke’s Law is described using the example of a spring.

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Resultant forces

When two or more forces act on an object, the resultant force can be found by adding up the individual forces.

A box on a table

A box rests on a table. Two arrows pointing in opposite directions act upwards and downwards from the point at which they meet on the table.

If the weight of the box (acting downwards) is 50 N and the normal reaction force (acting upwards) is 50 N, the forces are balanced. The resultant force is 0 N.

An object falling through the air

A box falls from the sky. Two arrows, equal in size and opposite in direction act upwards from the box and downwards from the box

If the weight of the box (acting downwards) is 50 N and the air resistance (acting upwards) is 20 N, the forces are unbalanced. The resultant force is 30 N downwards.

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Podcast: Forces and elasticity

In this episode, James Stewart and Ellie Hurer introduce forces and elastic potential. They also explain the key equations needed to understand the relationship between forces and extension.

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Newton's First Law

According to Newton's First Law of motion, an object remains in the same state of motion unless a resultant force acts on it. If the resultant force on an object is zero, this means:

  • a stationary object stays stationary

  • a moving object continues to move at the same (at the same speed and in the same direction)

Examples of objects with uniform motion

Newton's First Law can be used to explain the movement of objects travelling with uniform motion (constant velocity). For example, when a car travels at a constant speed, the driving force from the engine is balanced by resistive forces such as air resistance and friction in the car's moving parts. The resultant force on the car is zero.

Other examples include:

  • a runner at their top speed experiences the same air resistance as their

  • an object falling at terminal velocity experiences the same air resistance as its weight

The image shows a box with two arrows of equal size and length extending out from each side.
Figure caption,
If the forces acting on an object are balanced, the resultant force is zero

Examples of objects with non-uniform motion

Newton's First Law can also be used to explain the movement of objects travelling with non-uniform motion. This includes situations when the speed, the direction, or both change. For example, when a car accelerates, the driving force from the engine is greater than the resistive forces. The resultant force is not zero.

Other examples include:

  • at the start of their run, a runner experiences less air resistance than their thrust, so they accelerate

  • an object that begins to fall experiences less air resistance than its weight, so it accelerates

The image shows a box with two arrows extending, one from each side. The left arrow is much shorter than the right arrow, representing the unbalanced forces acting on the object.
Figure caption,
If the forces acting on an object are not balanced, the resultant force is not zero

Extended syllabus content: F = ma equation

If you are studying the Extended syllabus, you will also need to recall and use the equation F = ma. Click 'show more' for this content:

Extended syllabus content: Motion in a circular motion

If you are studying the Extended syllabus content, you will also need to describe motion in a circular motion. Click 'show more' for this content:

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Friction

is a . These are that act between two objects that are physically touching each other. Examples of other contact forces include and .

When a contact force acts between two objects, both objects experience the same size force, but in opposite directions. This is Newton's Third Law of Motion.

Solid friction

Two solid objects sliding past each other experience forces. For example, a box sliding down a slope.

A box rests on an incline. There are three arrows; one acting vertically downwards from the centre of the box’s base. One arrow acts perpendicular to the incline. One arrow acts up the incline.

Solid friction forces on two objects always act in the opposite directions to their overall movement.

Solid friction forces can slow objects down and change their direction. They can also produce heat when the store in the objects is being transferred to their store. For example, the friction between a match and its box produces enough heat to light it, or rubbing your hands together on a cold day.

Frictional forces are often useful. For example, people can walk because of frictional forces between their shoes and the pavement. Frictional forces also allow cars to accelerate, brake and turn corners.

Some frictional forces are not useful. For example, parts of car engines that touch produce friction which can generate heat and wear them away. Here friction is often reduced by using like engine oil.

Without a force propelling an object it will gradually stop because of frictional forces. This is Newton’s First Law of motion.

Drag

Drag is the frictional force that acts upon an object as it moves through a gas or liquid. is a type of drag which occurs when an object moves through air. For example, a skydiver falling from a plane.

A sky diver falling from a plane
Image caption,
A skydiver falling from a plane will slow down when they open their parachute.

A skydiver will slow when they open their parachute. This increases their surface area and so increases drag which slows them down.

More drag occurs when objects are moving at higher speeds. A submarine has more drag to work against when it is moving more quickly. The same is true for a car and air resistance. Keeping at these higher speeds requires more energy from the engines.

The effects of drag can be minimised by streamlining moving objects. Formula 1 teams make cars with minimal drag to increase their speeds.

Turning off the engine stops the forward force. Without this the vehicle (or other object) would gradually stop because of drag. This is unless it was in space where there is no drag.

A sky diver falling from a plane
Image caption,
A skydiver falling from a plane will slow down when they open their parachute.

Video: Friction

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Moments

A force or system of forces may cause an object to turn. A is the turning effect of a force. Moments act about a point in a clockwise or anticlockwise direction. The point chosen could be any point on the object, but the - also known as the fulcrum - is usually chosen.

A plank balances on a pivot. There are identical boxes, or objects at each end of the plank, with two arrows point downwards from the boxes. Curved arrows at the ends indicate possible rotation.
Figure caption,
The anticlockwise moment acts downward on the left, and the clockwise moment acts downwards on the right.

Using moments

Spanners and levers both use moments.

Spanners

Spanners are used to turn nuts and bolts. If you need to undo a nut that is very tight, you can:

  • use a short spanner and apply a large force

or

  • use a long spanner and apply a small force

Using the longer spanner increases the distance from the pivot. This reduces the amount of force needed to undo the nut from the bolt.

A person using a screwdriver to open a can of paint
Image caption,
A screwdriver can be used as a lever

Levers

Removing the lid from a can of paint requires a large lifting force on the lid. A screwdriver acts as a lever.

The pivot is the edge of the can and this is very close to where the strong push is needed to lift the lid to open the can.

A screwdriver with a long handle means that you can push down on the handle of the screwdriver with a small force and still open the can.

A person using a screwdriver to open a can of paint
Image caption,
A screwdriver can be used as a lever

Calculating the moment of a force

The magnitude of a moment can be calculated using the equation:

moment of a force = force × distance

\(M = F~d\)

This is when:

  • moment (M) is measured in newton-metres (Nm)

  • force (F) is measured in newtons (N)

  • distance (d) is measured in metres (m)

Key fact: it is important to remember that the distance (d) is the perpendicular distance from the pivot to the line of action of the force (see diagram).

A plank balances on a central pivot, with boxes at each end. Lines cross through the middle of the boxes and pivot, with arrows showing the distance between them..
Figure caption,
The perpendicular distance is the shortest distance between the pivot and the line of action of the force

Example

A simple image of a door with handle shows a curved arrow indicating that handle is pushed down on, or turned.

A force of 15 N is applied to a door handle, 12 cm from the pivot. Calculate the moment of the force.

First convert centimetres into metres:

12 cm = 12 ÷ 100 = 0.12 m

Then calculate using the values given in the question:

\(M = F~d\)

\(M = 15 \times 0.12\)

\(M = 1.8~Nm\)

Question

A force of 40 N is applied to a spanner to turn a nut. The perpendicular distance is 30 cm. Calculate the moment of the force.

A spanner is turning nut. The curved arrow at bottom of spanner indicates direction of turn.

Moments and balanced objects

If an object is balanced, the total clockwise moment about a pivot is equal to the total anticlockwise moment about that pivot.

Key fact: if the object is balanced: total clockwise moment = total anticlockwise moment

The diagrams show two examples of balanced objects where there is no rotation.

A plank sits on a pivot like a see-saw. Boxes sit at each end of the plank, with two equal arrows pointing downwards from the boxes.
Figure caption,
A balanced see-saw
There is a cross section of a trough with a ball at the lowest point inside.
Figure caption,
A ball at the bottom of a trough

For a balanced object, you can calculate:

  • the size of a force, or

  • the perpendicular distance of a force from the pivot

Example

A parent and child are at opposite ends of a playground see-saw. The parent weighs 750 N and the child weighs 250 N. The child sits 2.4 m from the pivot. Calculate the distance the parent must sit from the pivot for the see-saw to be balanced.

child's moment = force × distance

250 N × 2.4 M = 600 Nm

Parent's moment = child's moment

Rearrange \(M = F~d\) to find d for the parent:

\(d = \frac{M}{F}\)

Then calculate using the values:

\(d = \frac{600~Nm}{750~N}\)

\(d = 0.8~m\)

Extended syllabus content: Applying the principle of moments

If you are studying the Extended syllabus, you will also need to be able to apply the principle of moments to other situations. You will also need to describe an experiment to demonstrate that there is no resultant moment on an object in equilibrium. Click 'show more' to see this content.

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Centre of gravity

Position

Depending on the object's shape, its centre of gravity can be inside or outside.

Regular shapes

A metre rule is a uniform and regular shape, therefore its centre of gravity, G, is at its centre ie, at the 50 cm mark.

The metre rule balances freely at its centre of gravity.

rectangle showing centre of gravity. Labelled 0cm to 100 cm.

Position of centre of gravity (G)

Regular shapes - A metre rule is uniform and a regular shape, therefore its centre of gravity, G, is at its centre - ie, at the 50cm mark. The metre rule balances freely at its centre of gravity.

rectangle showing centre of gravity. Labelled 0cm to 100 cm.
circle with centre of gravity labelled as g

Disc

The centre of gravity G is the centre of the circle, where the diameters cross.

circle with centre of gravity labelled as g
ring with centre of gravity

Ring

The centre of gravity, G, is at the centre of the ring, where the diameters cross. In this case, the centre of gravity is not part of the ring but in the space at the centre.

ring with centre of gravity
triangle with centre of gravity

Irregular shapes

The centre of gravity, G, is where the medians cross. It is closer to the base than the top, because there is more weight towards the base.

triangle with centre of gravity
hockey stick

Non-uniform

A hockey stick is non-uniform - it is thicker and heavier on one end. Its centre of gravity, G, is not at its centre but will be closer to the heavier, curved end.

hockey stick

Finding the centre of gravity

A flat shape is called . A simple experiment can be used to find the of a plane lamina.

Equipment: Plane lamina, , pencil

Method:

  1. A small hole is made at the top of the plane lamina.

  2. The plane lamina is hung from this hole to allow it to .

  3. The plumb line is also hung from here and will fall vertically downwards.

  4. A dotted line is draw along the plumb line to the mass.

  5. The second hole can be made anywhere close to the edge of the shape and does not specifically need to be at the bottom.

  6. The above steps are repeated.

  7. The centre of gravity is where the lines cross.

Finding the centre of gravity experiment - a weight hangs from a plane lamina. A weight hangs from the bottom with the line of centre of gravity drawn through the middle vertically.
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Stability

Stability is a measure of how likely it is for an object to topple over when pushed or moved.

Stable objects are very difficult to topple over, while unstable objects topple over very easily.

Key fact: an object will topple over if its centre of gravity is 'outside' the base, or edge, on which it balances.

Two cars on their side

Key fact: for an object to be stable it must have:

  • a wide base

  • a low centre of gravity

Objects with a wide base, and a low centre of gravity, are more stable than those with a narrow base and a high centre of gravity.

The yellow car has a wider wheel base and lower centre of gravity than the blue car.

It is more stable.

The wheel acts as the for the car.

The weight has a turning effect or moment, which causes the car to topple over or fall back.

cars on their side

A double decker bus is stable as it has a:

  • low centre of gravity because of its low, heavy engine and heavy bottom deck;

  • wide wheel base.

A traffic cone is stable as it has a:

  • low centre of gravity G because of its heavy base;

  • wide base.

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Quiz

Test your knowledge with this quiz on forces.

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Teaching resources

Are you a physics teacher looking for more resources? Share this selection of short videos with your students:

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