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 μk = 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 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.

Accepted Answer

[latex]\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}[/latex]

Thus,

[latex](v_B)_2 = 2.909 ft/s ightarrow \ (v_A)_2 = -9.091 ft/s = 9.091 ft/s \leftarrow[/latex]

Block B:

[latex]\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}[/latex]

Question : A 1-lb ball A is traveling horizontally at 20 ft/s when it s...

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