# Problem 8-86 Inelastic collision

A large ball of modeling clay $(\text{mass}\; 4.5 \times 10^2\; g)$ is rolled on a tabletop so that it collides with a stationary small wooden box $(\text{mass} \; 7.9\times 10^2\; g)$. The collision is completely inelastic, and the ball and box then slide on the table for a distance of $5.1 \;cm$. If the speed of the ball is $2.2\; m/s$ just before the collision, determine: (a) the speed of the ball and box just after the collision (b) the magnitude of the friction force acting on the ball and box.

Accumulated Solution The situation is illustrated in the above figure.

It looks as if this is a problem in which conservation of momentum doesn't apply, since things are moving at the beginning (system has momentum) an then everything comes to rest (momentum = 0). Clearly momentum is not conserved because of the action of external forces (friction). But let's divide the question into 2 parts.

1. The collision itself in which only the clay and the box interact (impact takes place so fast that effect of the external forces is negligible).
2. The subsequent motion of the combined mass slowing down due to friction.

Let's deal with part 1 first. The problem states it is an  an elastic collision so:

(A)   Momentum is conserved.

(B)   Kinetic energy is conserved.

(C)   Neither is conserved.

(D)   Both are conserved.