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Forces and Motion

The Change in Momentum for a Car Stopped by Braking.

How much Force is needed to Stop a Car?

A moving car which comes to a stop has a change in momentum.

In example 1 a car uses its braking force to bring it to a stop.
In example 2 on the next page
the same car is brought to a stop by crashing into a wall.

Example 1.

A car has a mass of 1000 kg and moves with a velocity of 18 m/s.

The driver brings the car to a stop in 15 seconds.
What braking force is applied?

Change in momentum = Force x time.
or       mv - mu = F x t.

mv = final momentum (the one it ended up with)
mu = initial momentum (the one it started with)
t = time

Final momentum
m x = 1000 x 0 because the car stopped.
= 0
kgm/s.

Initial momentum
m x u = 1000 x 18
= 18000 kgm/s.

The change in momentum mv - mu
= 0 - 18000
= - 18000 kgm/s.
(The negative sign only shows that the car lost momentum).

Change in momentum = Force x time.
18000
= F x 15
F = 18000 ÷ 15
= 1200 N.

The braking force needed to stop the car in 15 seconds is 1200 N.

A car that is stopped safely by braking experiences a much
smaller force than a car that crashes. In the examples
shown on this page and the next, the force is 15 times smaller
because the car took 15 times longer to stop.
This has implications for driver and passenger safety.

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