State Hooke’s Law for a spring.
A spring is compressed by a force applied to it. Figure 4.1 shows how the force $F$ changes with compression $x$. Calculate the spring constant.
Show that the work done in compressing the spring by $36\,\text{mm}$ is $0.81\,\text{J}$.
A force is applied to compress a spring. Figure 4.1 shows the variation of force $F$ with compression $x$.
A child’s toy uses the spring in (b) to launch a small ball vertically upwards. The ball has a mass of $25\ \text{g}$. Figure 4.2 shows the toy.
The spring in the toy is compressed by $36\ \text{mm}$. The spring is then released. Assume that all the strain energy stored in the spring becomes kinetic energy of the ball. Using the answer from (b)(ii), calculate the speed at which the ball leaves the spring.
Determine the compression of the spring needed for the ball to leave the spring with twice the speed found in (i).
Find the ratio $\dfrac{\text{maximum possible height for compression in (i)}}{\text{maximum possible height for compression in (ii)}}.$