Question

Two gliders are set in motion on a horizontal air track. A spring of force constantis attached to the back end of the second glider. As shown in Figure P9.75, the first glider , of mass, moves to the right with speed, and the second glider, of mass, moves more slowly to the right with speed . Whencollides with the spring attached to, the spring compresses by a distance , and the gliders then move apart again. In terms of ,,,, and, find (a) the speed at maximum compression, (b) the maximum compression, and (c) the velocity of each glider afterhas lost contact with the spring.

Figure P9.75

Short answer

$$\begin{gathered} \left(a\right)v=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2} \\ \left(b\right)x_m=\left(v_1-v_2\right)\sqrt{\frac{m_1{m}_2}{k\left(m_1+m_2\right)}} \\ \left(c\right)v_{1f}=\frac{\left(m_1-m_2\right)v_1+2m_2{v}_2}{m_1+m_2} \\ {v}_{2f}=\frac{2m_1{v}_1+\left(m_2-m_1\right)v_2}{m_1+m_2} \end{gathered}$$

Step-by-step solution

Explain given information

Consider that two gliders are placed on a horizontal air track that are set in motion. A force constant $k$is attached to the back end of the second glider. Consider the Figure P9.75 that shows that mass of the of the each glider is mentioned as$m_1$and$m_2$respectively. The glider with $m_1$moves right with speed$v_1$and the glider with moves right with speed$v_2$. When the glider$m_1$collides with the spring attached to

and the compressed spring distance is $x_{max}$$x_{max}$.

In terms of and k , find the speed  at maximum compression