Find the ratio $\dfrac{\text{kinetic energy of the child at Y when the resistive force is }76\,\text{N}}{\text{kinetic energy of the child at Y if there is no resistive force}}$.
Use the result from (a) to find the ratio $\dfrac{\text{speed of the child at Y when the resistive force is }76\,\text{N}}{\text{speed of the child at Y if there is no resistive force}}$.
Calculate the length of the slide from X to Y.
At the lower end Y of the slide, the child is stopped by a board, as shown in Fig. 4.2. A spring links the board to a fixed point. The spring follows Hooke’s law and has a spring constant of $63\,\text{N m}^{-1}$. The child strikes the board, causing it to move to the right and compress the spring. The child’s speed becomes zero when the elastic potential energy of the spring has risen to its maximum value of $140\,\text{J}$. Calculate the maximum compression of the spring.
Calculate the percentage efficiency of the transfer of the kinetic energy of the child to the elastic potential energy of the spring.
The maximum compression of the spring is $x_0$. On Fig. 4.3, sketch a graph to display how the elastic potential energy of the spring varies with its compression $x$ from $x = 0$ to $x = x_0$. No numerical values are needed.