Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A child with mass $35\,\text{kg}$ is on a rope swing. Model the child as a particle $P$, and model the rope as a light inextensible string of length $4\,\text{m}$. At the start, $P$ is being held at an angle of $45^\circ$ to the vertical (see diagram).
(a)[4]
Assuming that there is no resistance force, determine the speed of $P$ after it has moved halfway along the circular arc from where it starts to its lowest point.
(b)[3]
Instead, there is a resistance force. The work done against the resistance force while $P$ moves from its initial position to its lowest point is $X\,\text{J}$. The speed of $P$ at its lowest point is $4\,\text{m s}^{-1}$. Find $X$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the loss of gravitational potential energy” …