Physics 9702 · AS & A Level · Gravitational potential energy and kinetic energy

Gravitational potential energy and kinetic energy — practice question

A pinball machine uses a spring to propel a small metal ball of mass $4.5 \times 10^{-2}\,\text{kg}$ up a ramp. The spring is compressed by $8.0 \times 10^{-2}\,\text{m}$ and maintained in equilibrium, as shown in Fig. 4.1. The ramp is inclined at an angle of $15^{\circ}$ to the horizontal.
(a)[2]

The spring obeys Hooke’s law and has a spring constant of $29\,\text{N m}^{-1}$. Calculate the elastic potential energy stored in the compressed spring.

(b(i))[3]

The spring is released and quickly extends back to its original length. Calculate the increase in gravitational potential energy of the ball when the spring returns to its original length.

(b(ii))[3]

The ball leaves the spring when the spring reaches its original length. Assume that all the elastic potential energy of the spring is transferred to the ball. Calculate the speed of the ball as it leaves the spring.

(c(i))[2]

The ball comes to rest on a horizontal trapdoor of negligible mass at a distance $d$ from its pivot. A force $F$ acts vertically downwards at a distance of $2.0\,\text{cm}$ from the pivot, as shown in Fig. 4.2. The trapdoor is in equilibrium when $F$ is $1.7\,\text{N}$. Calculate $d$.

(c(ii))[1]

Force $F$ is decreased from $1.7\,\text{N}$. State the direction of the resultant moment about the pivot on the trapdoor.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies $E = \tfrac{1}{2}kx^{2}$ or $E = \tfrac{1}{2}Fx$ with $F=kx$

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