# Completely inelastic collision

This is a problem I have thought about for a long time without any progress. Please give me a hint.

## Homework Statement

Cars B and C are at rest with their brakes off. Car A plows into B at high speed, pushing B into C. If the collisions are completely inelastic, what fraction of the initial energy is dissipated in car C? Initially the cars are identical.

## Homework Equations

$$p_{i}=p_{f}$$

## The Attempt at a Solution

The momentum is conserved and since it is a completely inelastic collision the cars are stuck to each other with velocity v, different from the initial velocity v0. $$mv_{0}=3mv$$ and $$v=\frac{v_{0}}{3}$$ and for car C
$$\frac{E_{C}}{E_{0}}=\frac{(v_{0}/3)^{2}}{v_{0}^{2}}=\frac{1}{9}.$$ Unfortunately the answer in my answer sheet is 1/6. What is wrong?

## Answers and Replies

Andrew Mason
Homework Helper
This is a problem I have thought about for a long time without any progress. Please give me a hint.

The momentum is conserved and since it is a completely inelastic collision the cars are stuck to each other with velocity v, different from the initial velocity v0. $$mv_{0}=3mv$$ and $$v=\frac{v_{0}}{3}$$ and for car C
$$\frac{E_{C}}{E_{0}}=\frac{(v_{0}/3)^{2}}{v_{0}^{2}}=\frac{1}{9}.$$ Unfortunately the answer in my answer sheet is 1/6. What is wrong?

The final mass is 3m moving at speed v0/3.

$$E_f = \frac{1}{2}3m\left(\frac{v_0}{3}\right)^2$$

So 2/3 of the energy is lost in the collisions. But there are two collisions:
The first is between A and B. What is the energy lost in that collision? The rest is lost in the second.

AM

Ok, so 1/2 of the energy is lost in the first collision and 1/6 in the second with a total loss of 2/3. My problem was that I did not understand the word dissipate. Maybe transmit was the word I confused it with? (My english is not so good, so I dont know.) So I guess my calculation was correct but not asked for. Thanks anyway Andrew.

Andrew Mason