A trolley T travels at $1.2\,\text{m s}^{-1}$ across a level frictionless surface. It collides with a stationary block attached to the end of a fixed spring, as shown in Fig. 3.1. The mass of T is $250\,\text{g}$. As T comes to rest, it compresses the spring by $5.4\,\text{cm}$. Fig. 3.2 shows how the force $F$ on the block varies with the spring compression $x$.
(a(i))[2]
From Fig. 3.2, determine the spring constant of the spring.
(a(ii))[2]
Using the information given, determine the work done by T as it compresses the spring by $5.4\,\text{cm}$.
(b(i))[2]
The spring then expands and makes T move in the opposite direction to its original motion. When T loses contact with the block, its speed is $0.75\,\text{m s}^{-1}$. From the time that T is in contact with the block, describe the energy changes.
(b(ii))[2]
Using the information given, determine the change in momentum of T.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $k = F/x$ or reciprocal gradient” …