Question

A 1,000 kg car is moving at 20 m/s, and slams into a building before coming to a halt.

How much momentum did the car have? If the crash took 0.5 s, how much force was exerted on the car by the building? (The impulse required to stop the car is F times t, and it is equal to the momentum. I gave you the time, so you can solve for the force.)

Answer 1

Hi there!

We can calculate linear momentum using the following:

`\large\boxed{p = m v}`

p = linear momentum (kgm/s)
m = mass (kg)
v = velocity (m/s)

Calculate:

`p = 1000 * 20 = 20000 kg(m)/(s)`

Now, we can relate force, time, and momentum with the following:

`\large\boxed{I = Ft}\\\\`

I = Impulse (kgm/s)
F = Force (N)
t = time (s)

Rearrange to solve for force:

`F = (I)/(t)`

The impulse is equal to the change in momentum. Since the car comes to a halt, all of its momentum is lost, so:


`I = \Delta p = p_f - p_i = 0 - 20000 = -20000`

Solve:

`F = (-20000)/(0.5) = \boxed{-40000N}`

**Negative force since the positive direction is towards the wall, and the negative direction is away from the wall.