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Forces and Motion

The Change in Momentum in a Car Crash.

What is the Size of the Force on a Car when it Crashes?

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

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

Example 2.

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

The car crashes into a wall and stops in 1 second.
What is the stopping force during the collision?

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 v = 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 1
F = 18000 ÷ 1
= 18000 N.

The car that crashes experiences a much larger force
than the car that stopped safely by braking.
The force is 15 times larger for the car that crashes
because the car stopped in
1/15th of the time.
This has implications for driver and passenger safety.

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