Additional Physics Topic 3 - Forces and Braking

When a vehicle is travelling at a constant speed, the forces add up to zero.  We saw this in Topic 1 and called it Newton's First Law (Newton I).

This does NOT mean that there are no forces.  The forces are balanced, and add up to zero.

Applying the Brakes

To slow an object down, you need to apply a force in the opposite direction to the velocity.  Velocity is appropriate, because there is a direction.  Consider this aeroplane.

If the pilot wants to slow down, he reduces the thrust from the engine.

 Question 1 What happens to the speed of the aeroplane?  Explain your answer in terms of the forces involved.

When large aeroplanes land, they slow down by applying reverse thrust, as well as applying the brakes.

Photo by Adrian Pingstone, Wikimedia Commons

Notice that as well as reverse thrust, there are spoilers sticking up from the wings to increase drag.  Also the flaps (hanging down) increase drag as well as increasing the lift, allowing the plane fly more slowly.

Brakes slow a car down by making extra friction, which is in the opposite direction to the movement of the car.  The acceleration is negative.

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Notice the slots in the brake disk.  This is because work is done to convert the kinetic energy in the car into heat.  In wet weather, you can see the brakes steaming.

The greater the speed, the bigger the braking force that is needed to stop a car in the same distance.  If you are driving at 50 km/h, it only needs a light force on the pedal to stop the car in 100 m.  If you are driving at 100 km/h it would need a much bigger braking force to stop the car within 100 m.

 Question 2 Where do rocket designers put retro rockets to make a spacecraft slow down?  Explain why.

Braking Force and Negative Acceleration

Newton's Second Law (F = ma) applies just as well to slowing down as it does to speeding up.

 Worked Example An aeroplane has a mass of 56 000 kg, and comes to rest from its landing velocity of 60 m s-1.  The time taken is 20 s.  What is the acceleration? What is the force acting on the aeroplane? Answer Acceleration = change in velocity ÷ time interval = (0 - 60) ÷ 20 = -3.0 m s-2 Force = mass × acceleration = 56 000 × - 3.0 = - 168 000 N

The minus sign means that the force is in the opposite direction to the velocity.

In this example I have deliberately used the terms velocity and acceleration to reinforce the idea of negative acceleration.  If speed is used, then the term deceleration is appropriate.  In the exam, look carefully at the question (which you should do anyway).  If the key words velocity and acceleration are there, there may be a mark available for having the minus sign. This is most likely in the higher tier paper.

Braking in cars

When you have to stop really quickly, for example a child runs out in the road in front of you, a significant proportion of the stopping distance is taken up with the "thinking distance".  There is a reaction time while you see the emergency, realise there is an emergency, and then put your foot on the brake.  During this time, the car is still travelling at the original speed.

In this case, the car is travelling at 14 m s-1.

During the thinking distance, the car is travelling at 14 m s-1 while the driver is realising that he is going to have to put the brakes in hard.

thinking distance (m) = speed (m s-1) × reaction time

Then the brakes come on and the car comes to a halt, hopefully before it hits the drum.

So the total distance can be worked out:

stopping distance (m) = thinking distance (m) + braking distance (m)

 Question 3 The reaction time of a driver is about 0.3 seconds.  What is the thinking distance if the car is travelling at 14 m s-1?

Have a look at the Highway Code.

The idea of thinking distance is shown on the speed time graph below:

 Question 4 What is: (a) the thinking distance; (b) the braking distance; (c) the total distance; (d) the acceleration shown for the car in the above graph?

The graph shows the braking performance of a car in good condition on a dry road.  The braking distance will increase if:

• the car is in poor condition, especially if the tyres are worn down;

• the road is wet or greasy.

If there is ice, there is very little friction, and braking has to be done very carefully indeed.  Ice is one of the slipperiest substances known.

The higher the speed, the longer the braking distance.  If you double the speed the braking distance goes up by four times.  This is because you have four times the kinetic energy in the car.

Driver Impairment

Some people try to drive after have several drinks in the pub, or worse still, having taken drugs.  The kind of mayhem that results is shown in the picture below:

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Why is it so dangerous to drive while drunk?   Although people have a sense of well-being, alcohol has a depressing effect on the brain.  This results in:

• loss of inhibition, making people show off by driving faster, or more aggressively;

• loss of coordination;

• less appreciation of dangerous situations;

• much slower reaction time when an emergency arises.

Using a mobile telephone while driving can impair the driver even more than alcohol.  There have been serious or even fatal accidents caused in this way, or, even worse, texting.

Now look at this graph to see how much longer it takes a drunk driver to react:

 Question 5 What is the reaction time of the drunk driver?  How much further does he travel?

The Police have campaigns at Christmas time and other times of the year to catch drivers who have had too much to drink.  And there are always people who get caught.  They are breathalysed, and, if over the limit, they will be arrested and charged.  The Law rightly takes a dim view of drinking and driving; it is completely unacceptable.  Innocent people get injured or even killed.  The least a drunk driver can expect is a heavy fine and losing their licence for at least a year.  Even when they can drive again, they can expect to pay massive insurance premiums for minimum cover for several years after.  On average, the premium is doubled.  If anyone is killed, a long prison sentence will result.

Pilots of aeroplanes and train drivers also are strictly forbidden to drink while on duty, or to present themselves while under the influence of alcohol, including a hangover.

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