Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A light inextensible rope has block $A$, of mass $5\text{ kg}$, at one end and block $B$, of mass $16\text{ kg}$, at the other. The rope runs over a smooth pulley fixed at the top of a rough plane inclined at an angle of $30^{\circ}$ to the horizontal. Block $A$ is kept at rest at the bottom of the plane, while block $B$ hangs below the pulley (see diagram). The coefficient of friction between $A$ and the plane is $\frac{1}{\sqrt{3}}$. Block $A$ is released from rest and the system begins to move. After each block has moved a distance of $x\text{ m}$, each has speed $v\,\text{m s}^{-1}$.
(i)[1]
State the gain in kinetic energy of the system, in terms of $v$.
(ii(a))[2]
Find, in terms of $x$, the loss of gravitational potential energy of the system.
(ii(b))[3]
Find, in terms of $x$, the work done against the frictional force.
(iii)[2]
Show that the result is $21v^2 = 220x$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gain in kinetic energy is $10.5v^2\text{ J}$” …