A metal ball with mass $40\,\text{g}$ drops vertically onto a spring, as shown in Fig. 4.1. The spring is mounted so that it stands upright. When the ball touches the spring, its speed is $2.8\,\text{m s}^{-1}$. As the spring is compressed, the ball is brought to rest.
(a)[2]
Show that the ball’s kinetic energy at the instant it contacts the spring is $0.16\,\text{J}$.
(b(i))[2]
Fig. 4.2 shows how the force $F$ on the spring changes with the spring compression $x$. When the ball stops, the spring reaches its greatest compression, $x_B$. The spring constant is $800\,\text{N m}^{-1}$. Use Fig. 4.2 to determine $x_B$.
(b(ii))[2]
Show that the kinetic energy from (a) is not all changed into elastic potential energy in the spring.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying $KE = \tfrac{1}{2}mv^2$” …