Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
ABCD is a semi-circular cross-section, in a vertical plane, of the inner surface of half a hollow cylinder of radius $2.5\,\text{m}$, fixed so that its axis is horizontal. AD lies horizontally, B is the lowest point of the cross-section, and C is $1.8\,\text{m}$ above the level of B (see diagram). A particle $P$ of mass $0.8\,\text{kg}$ is released from rest at A and reaches instantaneous rest at C.
(i)[2]
Find the amount of work done on $P$ by the resistance to motion while $P$ moves from A to C.
(ii)[3]
The work done on $P$ by the resistance to motion while $P$ travels from A to B is $0.6$ times the work done while $P$ travels from A to C. Find the speed of $P$ when it passes through B.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying $\text{PE loss} = 0.8g(2.5 - 1.8)$ gives $5.6\text{ J}$” …