The graph in Fig. 3.1 shows how the force $F$ changes with extension $x$ for a spring. One end of a spring with an unstretched length of $0.40\ \text{m}$ is fixed to a stationary point. A block of weight $2.5\ \text{N}$ is hung from the spring and then released, so it moves downward. At a certain moment, the spring’s length is $0.72\ \text{m}$. Take air resistance and the mass of the spring to be negligible.
(a(i))[2]
For the spring’s change in length from $0.40\ \text{m}$ to $0.72\ \text{m}$, use Fig. 3.1 to show that the spring’s elastic potential energy increases by $0.64\ \text{J}$.
(a(ii))[2]
Calculate the decrease in gravitational potential energy for the block with weight $2.5\ \text{N}$.
(b(i))[1]
Use the information in (a)(i) together with your answer to (a)(ii) to determine the kinetic energy of the block at the instant when the spring length is $0.72\ \text{m}$.
(b(ii))[2]
Use the information in (a)(i) together with your answer to (a)(ii) to determine the speed of the block at the instant when the spring length is $0.72\ \text{m}$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $E = \tfrac{1}{2}Fx$ or $E = \tfrac{1}{2}kx^2$ or area beneath graph” …