State Hooke’s law in words.
A spring is secured at one end. A compressive force $F$ is applied to the other end. The way the force $F$ changes with the compression $x$ of the spring is shown in Fig. 4.1. Show that the elastic potential energy of the spring is $0.64\,\text{J}$ when its compression is $16.0\,\text{cm}$.
The spring in (b) is used to launch a toy car along a track from point X to point Y, as shown in Fig. 4.2. At the start, the spring is compressed by $16.0\,\text{cm}$. The car of mass $0.076\,\text{kg}$ is held against one end of the compressed spring. When the spring is released, it propels the car forwards. The car leaves the spring at point X with kinetic energy equal to the initial elastic potential energy stored in the compressed spring. The car travels round a vertical loop of radius $0.12\,\text{m}$ and then passes point Y. Assume that friction and air resistance are negligible. Calculate: (i) the speed of the car at X (ii) the kinetic energy of the car when it is at the top of the loop (iii) the speed of the car at Y.
In practice, a resistive force caused by friction and air resistance acts on the car so that its kinetic energy at Y is $0.23\,\text{J}$ lower than its kinetic energy at X. Determine the average resistive force acting on the car during its motion from X to Y.