State Hooke’s law in words.
The way the force $F$ varies with compression $x$ for a spring is shown in Fig. 3.1. The spring is attached to the sealed end of a horizontal tube. A block is forced into the tube so that the spring becomes compressed, as shown in Fig. 3.2. The spring compression is $4.0\,\text{cm}$. The block has a mass of $0.025\,\text{kg}$.
Calculate the spring constant for the spring.
Show that compressing the spring by $4.0\,\text{cm}$ gives a work done of $0.48\,\text{J}$.
The block is then released and speeds up along the tube as the spring returns to its original length. The block exits from the end of the tube at a speed of $6.0\,\text{m s}^{-1}$. Calculate the kinetic energy of the block as it leaves the end of the tube.
Assume that the spring has negligible kinetic energy when the block leaves the tube. Determine the average resistive force acting on the block as it travels along the tube.
Determine the efficiency of the transfer of elastic potential energy from the spring to the kinetic energy of the block.