# Forces, Moments and Pressure

## Newton's Laws

#### Newton's First Law

Newton's First Law states that:

'Every body continues in a state of rest or uniform motion unless acted upon by an external force.'

This sounds really complicated... but isn't.

Imagine that you are playing table hockey. If you have not put your money in and you give the puck a hit, it doesn't travel very far. Friction stops it.

However, if you put your money in, air is pumped out of the holes in the table and so when you give the puck a flick, it will travel to the other end of the table. There is much less friction to slow the puck down. You need the end of the table to stop it. In both cases, a force starts and stops the puck, but a force is not needed to keep it moving at a steady speed.

So in other words, something without a net force acting on it will either stay still or move at a constant speed in a straight line until you apply a force to it.

When you apply a force to it, it will either:

• Speed up,
• Slow down,
• Change direction,
• (Or change shape).

#### F = ma

Also known as Newton's Second Law - you will have seen this equation during your course.

• F is the force in Newtons, N.
• m is the mass in kilograms, kg.
• a is the acceleration in m/s2.

This shows that if you keep the mass constant and double the applied force the acceleration will double.

If you plot a graph of force against acceleration it will look like this:

You can see here that force is proportional to acceleration. As you double the force the acceleration doubles, as you triple the force the acceleration triples.

If you plot a graph of acceleration against mass it will look like this:

You can see here that if you keep the force constant and increase the mass the acceleration will fall. Acceleration is inversely proportional to mass. If you double the mass the acceleration will halve.

It is helpful if you can rearrange this equation. The triangle for this is as follows:

Some examples:

1. A 500kg car accelerates at 3 m/s2.

How much force is exerted by the wheels to accelerate the car?

• Write down the formula: F = ma
• Plug in the numbers: F = 500 x 3
• Write down the answer: F=1500N

Note: Don't forget the units!

2. A 500kg car is accelerated by a force of 2000N. What is its acceleration?

Important point: The equation works in exactly the same way for deceleration as it does for acceleration!

## Behaviour of Solids

#### Hooke's Law, elastic and plastic behaviour

(Note: Plastic behaviour is sometimes called inelastic behaviour.)

In the 1600s, a scientist called Robert Hooke discovered a law for elastic materials.

An elastic material is one that will return to its original shape when the force applied to it is taken away.

A plastic (or inelastic) material is one that stays deformed after you have taken the force away.

If you apply too big a force a material will lose its elasticity.

Hooke discovered that the amount a spring stretches is proportional to the amount of force applied to it. This means if you double the force its extension will double, if you triple the force the extension will triple and so on.

Click on the weights below to see what happens:

The elastic limit can be seen on the graph. This is where the graph stops being a straight line. If you stretch the spring beyond this point it will not return to its original shape.

You can write Hooke's law as an equation:

F = kx

where:

• F is the applied force (in newtons, N),
• x is the extension (in metres, m) and
• k is the spring constant (in N/m).

The spring constant measures how stiff the spring is. The larger the spring constant the stiffer the spring. You may be able to see this by looking at the graphs below:

Elastic behaviour is very important in car safety, as car seatbelts are made from elastic materials. However, after a crash they must be replaced as they will go past their elastic limit.

Why have seat belts that are elastic?

Why not just have very rigid seatbelts that would keep you firmly in place?

The reason for this, is that it would be very dangerous and cause large injuries. This is because it would slow your body down too quickly. The quicker a collision, the bigger the force that is produced.

This can be seen very plainly by comparing the effect of kicking a football, which squashes as you kick it giving a big collision time, followed by kicking a brick. The brick doesn't squash, giving a very quick collision time and a very painful foot.

Press play to view this happening:

This is why airbags and crumple zones can reduce injuries (these are both parts of a car designed to squash rather than be rigid).

So to reduce injuries in a collision, always slow down in as long a time as possible. This is why you bend your legs when landing after a jump and why parachutists roll when they hit the ground.

## Forces and Pressure

#### In solids

1. Pushing a drawing pin into a wall pointy end towards the wall.
2. Pushing a drawing pin into a wall pointy end towards your thumb.

Two similar activities with two very different results.

The reason for this is the difference in pressure. Assuming the same force is applied, each case would have a different pressure acting on the thumb. In the first diagram the thumb pushes on a large area so the force is spread out and the pressure is low. In the second diagram the force is concentrated on a small area so the pressure is much higher.

If a force is applied over a smaller surface area you get a larger pressure.

Pressure can be calculated using the following equation:

Force will be in newtons, N.

Area will be in either m2 or cm2.

If the area is in m2 then the pressure will be measured in Pascals or N/m2. If the area is in cm2 then the pressure will be in N/cm2.

Example:

A lump of cheese of weight 20N stands on a table. It is a cubic lump with an area of 10cm2.

What pressure does it exert on the table?

Note: Don't forget the units!

#### In liquids

When it comes to pressure in liquids, there are 3 rules that you need to remember:

1. Pressure increases with depth

Have you ever noticed that when you dive down to the bottom of a swimming pool, your ears start to hurt? The further you dive down, the more it hurts.

This is because the pressure in a liquid increases as you go further below the surface of the liquid.

A common example in exams is this - a can full of water with holes down the sides. Notice how the further down the hole is, the faster the water comes out because the higher the pressure is in that part of the can.

Here are some other common examples. Can you explain them?

• Water comes out of a downstairs tap faster than an upstairs tap.
•
• Dam walls have to be thicker at the bottom than at the top.

You always get these ideas in any movie that has a submarine in it. You can guarantee that at some stage during the film, the sub will go too deep! Alarms will sound, people start to sweat, look nervous and the sub will creek and groan. Sometimes, the water will burst in and the sub will 'implode' (that means explode inwards rather than outwards).

This is due to the fact that the pressure from the water outside the submarine increases as the sub goes deeper and deeper until the structure of the sub isn't strong enough to resist - and it is crushed.

2. Pressure acts equally in all directions

To illustrate this:

• Grab a plastic bag.
• Fill it with water.
• Tie a knot in the top.
• Squeeze it.
• Then poke holes in the bag with a pin!
• Water goes everywhere! And that's the point.
• Water, from holes at the top of the bag, goes up.
• Water, from holes at the side of the bag, goes sideways.
• Water, from holes at the bottom of the bag, goes down.

This shows that the pressure in the water (which makes the water squirt out of the bag) is acting in all directions - not just downwards!

There's another example that helps to explain this. Remember when you are swimming at the bottom of the pool and your ears are hurting. It doesn't matter what you do with your head - turn left, right, twist it up or down - your ears hurt just as much. The water is pushing in on them from all sides equally - not just downwards.

3. Pressure is transmitted through liquids

You can't squash liquids. We say that they are 'incompressible'.

Fill a syringe with water. Put your thumb over the nozzle and press the plunger. It won't move. The water in the syringe can't be compressed.

Do the same thing with a syringe full of air and you can easily squash it. Air is compressible.

The fact that you can't compress liquids is extremely useful. It means that pressure can be transmitted through liquids.

An example - you connect two syringes together with a pipe and then fill them with water. Press one plunger in - and the other one comes out. That's because you have transmitted pressure from one plunger to the other.

This is used in hydraulics.

Hydraulics

All hydraulics systems work because the pressure is the same throughout the system.

Think about it. If you are driving a car along a motorway, you can stop it quite quickly by pushing gently on the brake pedal.

Now here's an alternative. You are driving a car along a motorway and you decide to stop. So you open the door, and, using the same force as above, gently press down on the tarmac with your foot.

(P.S: In case you need to be told - don't try this!!!)

You won't be surprised to learn that the car doesn't stop nearly as quickly. And, you wreck your trainers!

So how does the car turn the small force that you apply to the brake pedal into the huge force needed to stop a speeding car?

If you look at the above diagram, you can see that the brake cylinder by the pedal (the master cylinder) that the driver presses is very narrow.

But the cylinders by the brakes (the slave cylinders) are very wide.

This means they apply a much larger force.

Why?

Because the pressure in the liquid is the same everywhere. So if the area is bigger in the slave cylinders the applied force must be bigger too.

This is easier to see with an example.

If you push the master cylinder with a force of 12N and it has an area of 3cm2.

Using the equation:

This means the pressure in the master cylinder must be:

Now, because pressure is the same throughout the system, that means that the pressure in the slave pistons must also be 4N/cm2.

If the slave cylinders have an area of 12cm2, using the equation:

• Force = Pressure x area
• Force = 4 x 12
• Force = 48N

(Note: The pressure stayed the same.)

#### In gases

Although gases are compressible (squashy) they exert a pressure because of the gas particles bouncing off things. The pressure the air exerts at the surface of the Earth is about 100,000 Pa. Luckily, our bodies have evolved to cope with that pressure, or we would be squashed.

The diagram below illustrates how gas particles exert more pressure when the gas is squashed.

Both cylinders have the same number of particles in - and both sets of particles are going the same speed.

Notice that the particles in the small cylinder hit the walls more frequently - because there is less distance for the particles to cross from the top to the bottom of the cylinder.

Now remember that it is the collisions that cause the pressure - more collisions means more pressure. So the fact that there are more collisions in the small container means that the pressure is higher in the small container.

Boyle's Law

The diagram above explains why changing the volume of a gas sample changes the pressure of the gas. Boyle's Law is a way of calculating how much the pressure changes when the volume changes.

An eighteenth century scientist called Robert Boyle discovered that for a fixed mass of gas the pressure x the volume of the gas stays the same.

In other words, as you squeeze a gas its pressure will go up and its volume will get less.

Important point: The temperature and mass of gas must stay the same for this to be true!

We can write this as:

pressure x volume = constant

or

P1V1 = P2V2

where:

P1 is the pressure of the gas at the start,

V1 the volume of the gas at the start and

P2 and V2 the pressure and volume of the gas at the end.

This tells us if we double the pressure of a gas its volume will halve. If we reduce the pressure by one half, the volume will double.

Example:

Imagine a balloon full of air. The air's pressure is 10N/cm2 and its volume is 300cm3.

You squash the balloon to 200cm3 without any air escaping.

What is the pressure of the air inside the balloon?

Write down the formula:

P1V1 = P2V2

(Remember: P1 is the pressure at the start, V1 is the volume at the start, etc)

Plug in the numbers:

10 x 300 = P2 x 200

Rearrange the equation to give:

so

P2 = 15 N/cm2.

Remember: The temperature and mass of gas must remain the same for this to work!

## Moments

#### Why door handles are near the edge of doors.

Moments make things turn or rotate. They are caused by forces but are not forces themselves. Like forces, moments have a direction. We say they are either clockwise or anti-clockwise, to show which way they will make something turn.

The bigger the force causing the turning effect the bigger the moment will be.

The further the force is from the pivot the bigger the moment will be.

The size of a moment can be calculated using:

Moment = Force x Distance

• Force is measured in newtons, N.
• Distance is measured in either m or cm.
• If the distance is in m then the moment will be measured in Nm.
• If the distance is in cm then the moment will be measured in Ncm.

(Note: The force needs to be at right angles to the lever or rotating object.)

Here are some pictures involving moments.

For each picture:

Click on the moment and the direction that you think is correct then mark your answer.

In many situations there is more than one moment acting. To find the net or resultant moment the moments have to be added or subtracted, depending on their direction. Here is a worked example:

Moment due to A = 20 x 2 = 40 Nm anti-clockwise

Moment due to B = 10 x 1 = 10 Nm anti-clockwise

Moment due to C = 20 x 3 = 60 Nm clockwise

The total anticlockwise moment is 40 +10 = 50 Nm.

The total clockwise moment is 60 Nm.

So the resultant moment is 60 Nm - 50 Nm = 10 Nm clockwise.

Now here is one for you to try. Fill the correct numbers into the boxes:

## Exam-style Questions

1. a) State two effects a force can have on an object.

(2 marks)

b) Name each of the forces labelled P, Q and R.

(3 marks)

c) Describe the motion of the submarine.

(2 marks)

d) If the forces on the cyclist are balanced then describe its motion.

(1 mark)

e) State two ways of reducing the drag forces on the bicycle.

(2 marks)

(Marks available: 10)

Answer outline and marking scheme for question: 1

a) Change the objects shape, break the object, change the speed or direction of the objects motion.

(2 marks)

b) P = pushing force. Q = Weight / Gravitational force. R = Frictional force.

(3 marks)

c) Accelerating both up and forward.

(2 marks)

d) Balanced forces occur at a steady speed (and when stationary - less likely in this case).

(1 mark)

e) Oil wheels, Sit in a streamlined position, cycle downhill, use a smoother road.

(2 marks)

(Marks available: 10)

2. a) An Ice Hockey player hits a 2kg puck with a force of 24N and it moves off with an initial acceleration of 12 m/s2.

What could be done to make the puck move with higher acceleration?

(2 marks)

b) What force would be needed to give an acceleration of 9 m/s2?

(2 marks)

c) A sports car and a motorbike both have good acceleration.

The car is mass 1200 kg and provides a driving force of 7200 N. What is its acceleration?

(2 marks)

d) The bike is mass 300 kg and provides a driving force of 2700 N. What is its acceleration?

(2 marks)

e) If the car crashes and the driver is not wearing a seatbelt he will go through the windscreen.

Why is it wrong to say that he has been 'thrown forward'?

(2 marks)

(Marks available: 10)

Answer outline and marking scheme for question: 2

a) Provide more force from the stick or reduce the mass of the puck.

(2 marks)

b) Provide more force from the stick or reduce the mass of the puck.

Force = 2 x 9 = 18 N

(2 marks)

c) Acceleration = force / mass

For the car: accel = 7200 N / 1200 kg = 6 m/s2.

(2 marks)

d) For the bike: accel = 2700 N / 300 kg = 9 m/s2.

(2 marks)

e) The driver continues forward because without the seat belt there is no force to stop him until he hits the windscreen.

(2 marks)

(Marks available: 10)

3. a) An aid plane is flying over a remote part of Africa and it has to drop an aid package as there is no landing strip.

There are two forces on the falling package - its weight and air resistance.

What causes the weight?

(1 mark)

b) What causes the air resistance?

(1 mark)

c) A parachute opens as the package falls. How does the shape of the parachute help the drop?

(2 marks)

d) Which of the weight and air resistance is greater when the package first falls out of the plane?

(1 mark)

e) Which of the weight and air resistance is greater when the parachute on the package first opens?

(2 marks)

f) Describe a shape that would fall quickly through the air with low air resistance.

(1 mark)

g) Why does it make little difference if you fall out of a plane without a parachute at 700 m and at 7000 m?

(2 marks)

(Marks available: 10)

Answer outline and marking scheme for question: 3

a) Weight is caused by the gravitational attraction of the object to earth.

(1 mark)

b) Friction with the air causes air resistance.

(1 mark)

c) The large area of the parachute creates a lot of air resistance, which slows the descent.

(2 marks)

d) At first the weight is greatest.

(1 mark)

e) When the parachute opens the air resistance is greatest.

(2 marks)

f) A rounded or pointed shape will cut through the air with minimum air resistance.

(1 mark)

g) When you fall you reach a terminal velocity. This is at a low height so the speed at which you hit the ground will be the same at both heights.

(2 marks)

(Marks available: 10)

4. a) A car has to stop on a stretch of road. The overall stopping distance is made up of the thinking distance and the braking distance.

What exactly is the driver doing during the thinking distance?

(1 mark)

b) What exactly is the driver doing during the braking distance?

(1 mark)

c) Names two factors that affect the thinking distance.

(2 marks)

d) State two weather conditions that would affect the stopping distance.

(2 marks)

e) Why is oil on the road a danger?

(2 marks)

f) Name two safety features that a car has.

(2 marks)

(Marks available: 10)

Answer outline and marking scheme for question: 4

a) Driver is realising he must stop and moving his foot to the brake pedal.

(1 mark)

b) Driver is pressing the brake pedal.

(1 mark)

c) Tiredness, alcohol, drugs, medication, distractions in the car, driver experience.

(2 marks)

d) Ice, snow, rain, sleet, hail.

(2 marks)

e) Lubricant, which reduces the friction between wheels and road.

(2 marks)

f) Crumple zones, seat belts, side impact bars, air bags.

(2 marks)

(Marks available: 10)

5. The diagram shows a graph of velocity against time for the journey of a motorbike.

a) Between what times was the bike stopped at a traffic light?

(1 mark)

b) Between what times was the bike overtaking?

(1 mark)

c) What was the fastest speed reached?

(1 mark)

d) For how long was the bike travelling at this speed?

(1 mark)

e) Between what two bits of time was the bike accelerating?

(2 marks)

f) At 10 seconds the bike began to slow. What was the deceleration?

(2 marks)

g) How fast had the bike travelled in the first 15 seconds?

(2 marks)

(Marks available: 10)

Answer outline and marking scheme for question: 5

a) Between 15 and 25 s

(1 mark)

b) Between 40 and 45 s

(1 mark)

c) 17.5 m/s

(1 mark)

d) 5 seconds

(1 mark)

e) Between 25 and 30 s and between 35 and 40 s

(2 marks)

f) Deceleration = change in velocity / time

deceleration = 10 / 5 = 2 m/s/s

(2 marks)

g) Distance travelled equals the area under the graph.

Distance = (10 x 10) + (0.5 x 10 x 5) = 100 + 25 = 125 m

(2 marks)

(Marks available: 10)

6. A transit van is leaking oil and drips every two seconds. It leaves a pattern along a road as shown in the diagram.

a) Describe the motion of the van between S and T where the drips are equal distances apart.

(1 mark)

b) What is the velocity of the van between S and T?

(2 marks)

c) How is velocity different from speed?

(1 mark)

d) What is the velocity of the van between P and Q?

(1 mark)

e) Using earlier answers and the diagram, calculate the acceleration of the van.

(3 marks)

f) If the engine cut out and the brake was not applied state what would happen to the van and why.

(2 marks)

(Marks available: 10)

Answer outline and marking scheme for question: 6

(1 mark)

b) Velocity = displacement / time

velocity = 42 m / 6 s = 7 m/s

(2 marks)

c) Velocity is the speed in a specified direction.

(1 mark)

d) Vel = 24 / 6 = 4 m/s

(1 mark)

e) Acceleration = change in vel / time

The time between the start of PQ to the start of ST is 6 spaces, which is 12 seconds.

Acceleration = (7 - 4) / 12 = 0.25 m/s/s

(3 marks)

The van would decelerate to a stop because of friction.

(2 marks)

(Marks available: 10)

## What can Forces do?

#### What can forces do?

A force can do one of four things to an object:

1. Make it speed up - accelerate.
2. Make it slow down - decelerate.
3. Change its direction.
4. Change its shape.

If something is doing one of these four things there must be a net force acting upon it.

(Note: Other names for a net force are an unbalanced force or a resultant force.)

#### Net forces

What do we mean by a 'net' force?

Well, forces do not add up like normal numbers - you must take their direction into account as well. For example, if you were teetering on the edge of a cliff and someone applied a force to you, you would probably like the force applied in a certain direction.

It is easy to add up forces, just look at these three examples:

The unit we measure force in is the Newton, named after Sir Isaac Newton, which leads us onto Newton's first law.

## S-Cool Revision Summary

A force can do one of four things to an object:

1. Make it speed up - accelerate.

2. Make it slow down - decelerate.

3. Change its direction.

4. Change its shape.

If something is doing one of these four things there must be a net force acting upon it.

##### Newton's First Law

'Every body continues in a state of rest or uniform motion unless acted upon by an external force.'

Something without a net force acting on it will either stay still or move at a constant speed in a straight line until you apply a force to it.

##### F = ma

Newton's Second Law:

• F is the force in Newtons, N.

• m is the mass in kilograms, kg.

• a is the acceleration in m/s2.

This shows that if you keep the mass constant and double the applied force the acceleration will double.

##### Hooke's Law, elastic and plastic behaviour

F = kx

An elastic material is one that will return to its original shape when the force applied to it is taken away.

A plastic (or inelastic) material is one that stays deformed after you have taken the force away.

If you apply too big a force a material will lose its elasticity.

##### In solids

If a force is applied over a smaller surface area you get a larger pressure.

Pressure can be calculated using the following equation:

Force will be in newtons, N.

Area will be in either m2 or cm2.

If the area is in m2 then the pressure will be measured in Pascals or N/m2.

If the area is in cm2 then the pressure will be in N/cm2.

##### In liquids
1. Pressure increases with depth.

2. Pressure acts equally in all directions.

3. Pressure is transmitted through liquids.

##### Hydraulics

All hydraulics systems work because the pressure is the same throughout the system.

##### In gases

Although gases are compressible (squashy) they exert a pressure because of the gas particles bouncing off things.

##### Boyle's Law

For a fixed mass of gas the pressure x the volume of the gas stays the same.

In other words, as you squeeze a gas its pressure will go up and its volume will get less.

Important point: The temperature and mass of gas must stay the same for this to be true!

We can write this as:

Pressure x volume = constant or P1V1 = P2V2

##### Moments

Moments make things turn or rotate. They are caused by forces but are not forces themselves. Like forces, moments have a direction. We say they are either clockwise or anti-clockwise, to show which way they will make something turn.

The bigger the force causing the turning effect the bigger the moment will be.

The further the force is from the pivot the bigger the moment will be.

The size of a moment can be calculated using:

Moment = Force x Distance

Force is measured in newtons, N.

Distance is measured in either m or cm.

If the distance is in m then the moment will be measured in Nm.

If the distance is in cm then the moment will be measured in Ncm.

##### Distance

As we all know, the distance between two points is how far apart they are. In science, we normally use metres as our unit.

We often represent how the distance between two points changes using a distance:time graph.

##### Speed

Speed is how fast something is going. It is how quickly something covers a certain distance and can be worked out using the equation:

##### Acceleration

This is how quickly something gets faster. So if you were running and getting 1m/s faster every second you would have had an acceleration of 1 m per second per second. We normally write this 1 m/s2.

We work out by the equation: