# Momentum Conservation

## Homework Statement

A car of mass 1500kg is parked on a 30degree slope before rolling down a distance of 30m onto a flat section where it collides with a stationary car. The cars stick together and scrape along the road for 20m until they come to a rest. Calculate the velocity of the two combined cars immediately after the collision. Calculate the energy lost in the collision and the average coefficient of dynamic friction between the road and the two vehicles

## The Attempt at a Solution

Pythagoras gives that the first car will drop a vertical height of 15m.
So mgh=0.5mv^2 energy conservation for the first car when it reaches the bottom of the slope. So it's velocity at the bottom of the slope will be 17.15m/s

Then to find the velocity of the combined cars immediately after the collision I need to use conservation of momentum BUT I don't have the mass of the second car??
m1v1 +m2v2 = (m1+m2) v3
1500 * 17.15 + m2 *0 = (1500 +m2) * v3

How can I find the resultant velocity??

Chestermiller
Mentor
I guess they expect you to assume that the mass of the 2nd car is the same as that of the first car.

Chet

haruspex
Homework Helper
Gold Member
2020 Award
You will need to think carefully (even, 'carfully') in the second part.

So if I assume that the second car is the same mass I would get a final velocity of the combined cars after the collision to be 8.575m/s

For the energy lost during the collision would I just need to compare the initial kinetic energy of car 1 before impact with the final kinetic energy of the combined cars after collision?

Ek lost = 0.5 (m1+m2) v^2 - 0.5 *1500 *17.15^2 = 110 295J

Chestermiller
Mentor
You will need to think carefully (even, 'carfully') in the second part.
Excellent. You're right. You don't have to assume
So if I assume that the second car is the same mass I would get a final velocity of the combined cars after the collision to be 8.575m/s

For the energy lost during the collision would I just need to compare the initial kinetic energy of car 1 before impact with the final kinetic energy of the combined cars after collision?

Ek lost = 0.5 (m1+m2) v^2 - 0.5 *1500 *17.15^2 = 110 295J
yes