Problem 8-86 Inelastic collision - Part 3B

A large ball of modeling clay (mass 4.5x102 g) is rolled on a tabletop so that it collides with a stationary small wooden box (mass 7.9x102 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.

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

\(v{'}= \frac{m_1}{m_1 + m_2} v_1 = \frac{4.5 \times 10^2}{12.4 \times 10^2}2.2= 0.798\; m/s = 0.80\; m/s\)

Now for part 2 of the problem we simply have an object of mass \(m = 1.24\; kg\) with an initial velocity of \(v_0 = 0.798\; m/s\) slowing down because of the force of friction. The acceleration of the mass is given by:

(A)   \(v = v_0 + at\)

(B)   \(x = v_{0^t} + (1/2)at^2\)

(C)   \(v^2 = v_0{^2} + 2ax\)