At the instant the spring is contacted, the block has kinetic energy $110\,\text{J}$. Calculate the speed of the block as it makes contact with the spring.
The block’s gravitational potential energy falls by $20\,\text{J}$ as the spring reaches its greatest compression $x_0$. Show that $x_0$ is $0.37\,\text{m}$.
Assume that, while the spring is being compressed, every bit of energy lost by the block becomes elastic potential energy in the spring. Use the results from (a) and (b) to determine the maximum elastic potential energy of the spring. Show your working.
Fig. 3.2 displays the way the force $F$ on the spring changes with the compression $x$ of the spring. Use the information in (b) and your answer to (c) to show that the maximum force $F_0$ exerted on the spring by the block is $700\,\text{N}$.
Using the information in (d), determine the magnitude of the resultant force acting on the block at the instant the spring first brings it to rest.
Using the information in (d), determine the magnitude of the block’s acceleration at the instant the spring first brings it to rest.