Table of contents | |
Estimating Decelerating Forces | |
Factors Affecting Reaction Time | |
Factors Affecting Braking Distance | |
Braking & Friction | |
Braking Force & Speed |
Example: At 18 m/s (40 mph) the braking distance of a typical car of mass 1500 kg is about 24 m. Use this information to estimate the braking force for a typical car.
Step 1: List the known quantities
(i) Mass, m = 1500 kg
(ii) Braking distance, s= 24 m
(iii) Speed, v= 18 m/s
Step 2: State the relevant equation
Step 3: Rearrange for the braking force
Step 4: Substitute the values into the equation
Exam Tip: You should be able to deduce from the equation that the braking distance is proportional to the vehicle's speed2. Note, this actually doesn't apply at very high speeds because the brakes get hot and become less effective. This reduces the braking force, causing the braking distance to increase even further.
Example: The graph below shows how the thinking distance of a driver depends on the speed of the car.
(a) Describe the connection between thinking distance and speed.
(b) Some people drive when they are tired, despite warnings against doing so. Draw a new line on the graph to show how thinking distance varies with speed for a tired driver.
Part (a)
Step 1: Check if the line is straight and if it goes through the origin
(i) The graph shows a straight line through the origin
(ii) Therefore, the thinking distance is directly proportional to the speed of the carPart (b)
Step 1: Recall the factors which affect the thinking distance
Three additional factors affect the thinking distance, because they affect human reaction time:
(i) Tiredness
(ii) Distractions
(iii) Intoxication
Hence, a tired driver's reaction time is greater (i.e. it takes longer for them to react)
Step 2: Draw a line that shows greater thinking distance for the same speed
(i) At the same speed, a tired driver's thinking distance will be greater than a driver who is alert
(ii) This means a line should be drawn with a steeper gradient, as shown below:
Example: A car is travelling at 15 m/s when the driver applies the brakes. The car decelerates uniformly and stops.The mass of the car and the driver is 1500 kg, and together they have a total kinetic energy of 168 750 J.
(a) How much work is done by the braking force to stop the car and the driver?
(b) The braking force used to stop the car and the driver was 6000 N. Calculate the braking distance of the car.
Part (a)
Step 1: Recall the process of applying brakes to a vehicle
(i) The work done is the energy transferred from the car and driver to the brakes
(ii) This energy transfer is from kinetic energy to thermal energy
(iii) In this case, the car is brought to a complete stop, so 168 750 J of energy is transferred from kinetic energy to heating up the brakes (assuming all energy is transferred to heat only!)Part (b)
Step 1: State the equation for work done
Work done = Force × distance travelled (or W = Fs)
In this case, the force doing the work (transferring energy) is the braking force
Step 2: Rearrange the equation and solve for distance travelled
Distance travelled = Work done ÷ Force
Step 3: Substitute the values for work and force
Distance = 168 750 ÷ 6000 = 28.1 m
Hence the braking distance (the distance travelled by the car under the braking force) is 28.1 m
Exam Tip: If you are asked to explain why the temperature of the brakes increases when a vehicle stops, remember, work is done by the frictional force between the brakes and the wheel.It's a common mistake to write about the friction between the wheels and the road. This does happen, but in this case, the wheels heat up the road! The brake temperature increases because there is a transfer of energy from the car's kinetic energy to the thermal energy of the brakes.
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