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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 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 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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