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5.6 More on the physics of vehicle braking and kinetic energy

The mechanical process of braking primarily relies on friction between the brake pad and a steel disc (shown on the right). When you press the brake pedal the hydraulic system pushes pads onto the surface of the disc causing work to be done due to the resistive forces between the surfaces.

The resulting friction effect transfers energy from the car's kinetic energy store to the thermal energy store of the braking system which is eventually dissipated to the environment's energy store.

The friction does cause the brakes to heat up - the brake pads and disc must be able to withstand a high temperature - both are made of high melting alloys.

A little of the KE is lost as sound.

If the wheel tyres skid on the road, friction will generate thermal energy and the road and tyre increase in temperature.

Eventually all the kinetic energy of the road vehicle is dissipated to the thermal energy store of the surroundings.

 

So when the work is done between the brakes and the wheel discs kinetic energy is converted to thermal/heat energy.

The faster a vehicle is going, the greater its kinetic energy store and more work must be done to bring the car to a halt.

It also means a greater force must be applied to bring the vehicle to a halt within a certain braking/stopping distance.

 

The greater the braking force, the greater the deceleration.

Big decelerations can be dangerous because the brakes may overheat affecting their action AND there is a much greater chance of skidding, particularly if the road surface is slippery due to conditions already described.

 

To put the point about kinetic energy into context, study graph 2 below.

Graph 2 shows how the kinetic energy of a road vehicle (e.g. a car of 1200 kg) varies with its speed.

You can see that by doubling the speed, you quadruple the kinetic energy of the car, hence you have quadrupled the kinetic energy to be removed by braking.

This is because KE = ½mv². Its the speed² term that gives this crucial mathematical importance.

Assuming uniform deceleration and uniform decrease in the rate of reducing kinetic energy, means the braking distance is a function of kinetic energy and speed². See graph 3 now.

 

Graph 3 below shows the linear relationship between the kinetic energy of the car and braking distance (using the UK Highway Code data and a 1200 kg car).

This is a result of KE = ½mv² and the braking distance data assumes uniform deceleration and uniform decrease in the rate of reducing kinetic energy due to the friction of the brakes.

As already mentioned, the braking distance increases faster than the speed.

The total work done to stop a road vehicle is equal to the initial maximum kinetic energy of the vehicle.

Work done to halt vehicle = total KE of vehicle

= braking force x braking distance

W = F x d = KE = ½mv²   (in a nutshell !)

W = work in J to come to a halt, and all of the work is done by the brakes (assuming no skidding) via friction from the vehicles KE store to the thermal energy store of the brakes and environment

F = braking force in N (assumed to be constant for the vehicle brakes),

d = braking distance in m, m = mass of vehicle in kg, v = speed of vehicle in m/s

If you skid on a dry road, the rubber left on the road tells you the tyres were doing a bit of braking work too!

If we assume a constant braking force (maximum push on brake pedal) and since the kinetic energy of the car is proportional to speed², then the braking distance is proportional to the initial kinetic energy of the car.

That's what the work done equation says for a constant braking force:

KE BD and so does the graph.

 

An extra consequence:

If your car is full of people or a lorry is fully loaded, then the kinetic energy at a given speed is greater than if the vehicle only contained the driver.

Therefore, with extra mass in the vehicle, extra distance should be allowed for your braking distance because of the extra kinetic energy.

Examples of typical masses for road vehicles:

cars 1000 - 1500 kg;  large van/single decker bus ~9 000 -10 000 kg

loaded lorry ~30 000 - 40 000 kg (40 tonnes).

 

INDEX of physics notes on reaction times, stopping distances of road vehicles, Newton's 2nd Law, braking friction force, KE calculations

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Key points force and motion: Road safety - advanced calculations on braking distance

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations

These particular 'braking calculations are based on the equation

W = F x d = KE = ½mv²   (in a nutshell !)

W = work done in J to come to halt a moving vehicle, and the work is done by the brakes due to friction

F = braking force in N

(assumed to be constant for vehicle brakes as the driver presses down on the brake pedal),

d = braking distance in m, m = mass of vehicle in kg, v = speed of vehicle in m/s

I can add some example but I've Q3 in Part 5.8

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Keywords, phrases and learning objectives for the physics of road vehicles - braking distance and the kinetic energy of a moving vehicle

Know the connection between a road vehicle's braking distance and the kinetic energy of a moving road vehicle.

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INDEX of physics notes on reaction times, stopping distances of road vehicles, Newton's 2nd Law, braking friction force, KE calculations