Forces and Motion

Momentum - Car Stopping - 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 1.

A car has a mass of 1000 kg and travels 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 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 15
               F = 18000 ÷ 15
             = 1200 N.

The car that stopped safely by braking experiences a
much smaller force than the car that crashes.
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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