# 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.

- 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).
- 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.