A 1-lb ball A is traveling horizontally at 20 ft/s when it strikes a 10-lb block B that is at rest. If the coefficient of restitution between A and B is e = 0.6, and the coefficient of kinetic friction between the plane and the block is { \mu }_{ k } = 0.4, determine the time for the block B to stop sliding.
Question : A 1-lb ball A is traveling horizontally at 20 ft/s when it s...
\begin{aligned} (\underrightarrow{+}) \quad\quad & \Sigma m_1 v_1 = \Sigma m_2 v_2 \\ & (\frac 1 { 32.2 })(20) + 0 = (\frac { 1 } { 32.2 })(v_A)_2 + (\frac { 10 } { 32.2 })(v_B)_2 \\ & (v_A)_2 + 10(v_B)_2 = 20 \end{aligned} \\ \begin{aligned} (\underrightarrow{+}) \quad\quad & e = \frac { (v_B)_2 – (v_A)_2 } { (v_A)_1 – (v_B )_1 } \\ & 0.6 = \frac { (v_B)_2 – (v_A)_2 } { 20 – 0 } \\ & (v_B)_2 – (v_A)_2 = 12 \end{aligned}
Thus,
(v_B)_2 = 2.909 ft/s \rightarrow \\ (v_A)_2 = -9.091 ft/s = 9.091 ft/s \leftarrowBlock B:
\begin{aligned} (\underrightarrow{+}) \quad\quad & m\space v_1 \Sigma \int F\space dt = m\space v_2 \\ & (\frac { 10 } { 32.2 })(2.909) – 4t = 0 \\ & t = 0.226 s \end{aligned}](https://holooly.com/wp-content/uploads/2020/11/Screenshot_2020-11-08-Engineering-Mechanics-Dynamics-14th-Edition-Instructors-Solutions-Manual-by-Russell-C-Hibbeler-z-l...6.png)