Figure 4.1 shows how the force $F$ applied to a spring varies with extension $x$. The spring has a natural length of $0.080\,\text{m}$ and is hung vertically from a fixed point. A block is fixed to the lower end of the spring. The block is in equilibrium at position X when the spring length is $0.095\,\text{m}$. The block is then pulled vertically downward and kept at position Y so that the spring length becomes $0.120\,\text{m}$. The block is then let go and moves vertically upward from position Y back towards position X.
(a)[2]
Use Fig. 4.1 to find the spring constant of the spring.
(b)[2]
Use Fig. 4.1 to show that the spring's elastic potential energy decreases by $0.055\,\text{J}$ as the block moves from position Y to position X.
(c)[2]
The block has a mass of $0.122\,\text{kg}$. Calculate the increase in gravitational potential energy of the block for its movement from position Y to position X.
(d(i))[1]
Use the decrease in elastic potential energy given in (b) together with your result from (c) to find the block's kinetic energy as it passes through position X.
(d(ii))[2]
Use the decrease in elastic potential energy given in (b) together with your answer in (c) to determine the block's speed as it passes through position X.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $k = \dfrac{F}{x}$ or the gradient of the graph” …