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## 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 when car

C is struck? The cars are identical initially.

## Homework Equations

Collisions

## The Attempt at a Solution

First collision:

First collision:

Momentum is conserved and the collision is inelastic so ##mv_1 = 2mv_2##. The energy dissipated after the first collision

is ## Q_1 = \triangle K = \frac{1}{2} mv_1 ^2 - m v_2^2 = \frac{1}{4}mv_1^2 = \frac{1}{2} K_i ##

__Second collision:__

Momentum is conserved and the collision is inelastic so ##2mv_2 = 3mv_3##. The energy dissipated after the second collision is ## Q_2 = \triangle K = m v_2 ^2 - \frac{3}{2}m v_3^2 = \frac{1}{3}mv_2^2 = \frac{1}{12}mv_1^2 = \frac{1}{6} K_i ##

Total energy lost is ## Q = Q_1 + Q_2 = \frac{2}{3} K_i ## so the fraction of initial energy dissipated after C is struck is 2/3.

Is that correct?