Physics 9702 · AS & A Level · Gravitational potential energy and kinetic energy
Gravitational potential energy and kinetic energy — practice question
A pendulum is made of a solid sphere hanging from a fixed point P by a string, as illustrated in Fig. 3.1. The sphere moves to and fro. At one moment it is at the lowest point X, and its kinetic energy is 0.86\,\text{J} while its momentum is 0.72\,\text{N s} horizontally. After a short interval, it reaches position Y, where it is briefly at rest at the greatest vertical height h above X. The string remains the same length and has negligible mass. Air resistance can be ignored.
(a)[1]
On Fig. 3.1, draw a solid line showing the displacement of the centre of the sphere from X to Y.
(b)[3]
Show that the sphere has a mass of $0.30\,\text{kg}$.
(c)[2]
Calculate height $h$.
(d)[1]
The distance from point P to the sphere’s centre is $0.93\,\text{m}$. At position Y, the string makes an angle $\theta$ with the vertical. Show that $\theta$ is $47^{\circ}$.
(e)[2]
For the sphere at position Y, Calculate the moment produced by its weight about point P.
(f)[1]
State and explain whether the sphere is in equilibrium while it is stationary at position Y.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “solid straight line joining the sphere centre at X to the sphere centre at Y” …