Problem 8-86 Inelastic collision - Part 4B

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

FBD of before and after.

\(m_1v_1 + m_2v_2 = (m_1 + m_2)v' \quad \; \text{where}\; v_2 = 0 \\ v{'} = 0.80\; m/s\; \text{ (answer to part (a))} \\ v_2 = v_0{^2} + 2ax \\ a = -6.24 \;m/s\)

\(v_2 = v_0{^2} + 2ax \\ 0 = 0.798^2 + 2a(5.1 \times 10^{-2} \;m) \\ a = -6.24\; m/s\)

This deceleration is a result of the friction force which we determine from:

(A)   \(F = ma\)

(B)   \(F = \mu FN\)

(C)   \(F = (1/2)mv^2\)