Forces and Motion

Momentum - Car Crashing - Calculations.

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

In example 1 a car is using its braking force to bring it to a stop.
In example 2 a car is brought to a stop by crashing into a wall.

Example 2.

A car has a mass of 1000 kg and travels 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 Ns.      

Initial momentum m x u
   = 1000 x 18
    = 18000 Ns.

The change in momentum mv - mu
  = 0 - 18000
      = - 18000 Ns.
(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 by braking.
The force is 15 times larger
because the car stopped in 1/15th of the time.
This has implications for driver and passenger safety.

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