Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
Particles $A$ and $B$, with masses $m\text{ kg}$ and $3\text{ kg}$ respectively, are joined by a light inextensible string. Particle $B$ lies on a fixed plane inclined at an angle of $\sin^{-1}0.6$ to the horizontal ground. The string goes over a fixed smooth pulley at the top of the plane. Particle $A$ hangs vertically beneath the pulley and is $0.75\text{ m}$ above the ground (see diagram). The system is released from rest. In the motion that follows, $B$ travels up a line of greatest slope of the plane and does not reach the pulley. As $B$ moves up the plane, a constant resistance of magnitude $\frac{10}{3}\text{ N}$ acts against its motion. The speed of $A$ just before it hits the ground is $2\text{ m s}^{-1}$.
(main)[6]
Use an energy method in order to determine the value of $m$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “PE decrease of A: $\pm mg\times0.75$” …