Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
Particles $A$ and $B$, each with mass $0.3\,\text{kg}$, are joined by a light inextensible string. The string runs over a small smooth pulley fixed at the edge of a rough horizontal surface. Particle $A$ hangs freely while particle $B$ is kept at rest in contact with the surface. The coefficient of friction between $B$ and the surface is $0.7$. Particle $B$ is released and moves along the surface without reaching the pulley.
(i(a))[2]
Find, for the initial $0.9\,\text{m}$ travelled by $B$, the work done against the frictional force on $B$.
(i(b))[1]
Find, over the first $0.9\,\text{m}$ travelled by $B$, the loss of potential energy of the system.
(i(c))[2]
Find, for the first $0.9\,\text{m}$ of $B$’s motion, the gain in kinetic energy of the system.
(ii)[3]
At the instant when $B$ has moved $0.9\,\text{m}$ the string breaks. $A$ is at a height of $0.54\,\text{m}$ above a horizontal floor at this instant. Find the speed with which $A$ reaches the floor.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “From $F = \mu R$ and $\text{WD} = Fs$, e.g. $F = 0.7 \times 3$, $\text{WD} = 2.1 \times 0.9$” …