Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
Particles $A$ and $B$, with masses $0.3\,\text{kg}$ and $0.5\,\text{kg}$ respectively, are fastened to the two ends of a light inextensible string. This string passes over a fixed smooth pulley, attached between a horizontal plane and the top of an inclined plane. At the start, the particles are at rest, with $A$ on the horizontal plane and $B$ on the inclined plane, which is inclined at $30^\circ$ to the horizontal. The string is taut, and $B$ moves along the line of greatest slope of the inclined plane. A force of magnitude $3.5\,\text{N}$ acts on $B$ down the plane (see diagram).
(a)[5]
Since both planes are smooth, determine the tension in the string and the acceleration of $B$.
(b)[4]
Now suppose that both planes are rough. After each particle has travelled $0.6\,\text{m}$ from rest, the total work done against friction is $1.1\,\text{J}$. Use an energy method to determine the speed of $B$ after it has moved this distance down the plane. [Assume that the string is long enough that $A$ does not reach the pulley when it moves $0.6\,\text{m}$.]
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law to form equations, for example $T = 0.3a$ and $3.5 + 0.5g\sin 30 - T = 0.5a$” …