Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

Particles $A$ and $B$, with masses $6.5\text{ kg}$ and $m\text{ kg}$ respectively, are linked by a light inextensible string passing over a smooth pulley. The pulley is fixed at the top of a rough slope inclined at angle $\alpha$ to the horizontal ground, where $\tan \alpha = \frac{5}{12}$. $A$ rests on the rough slope and $B$ hangs beneath the pulley (see diagram). The coefficient of friction between the slope and $A$ is $0.4$.
(a)[7]

Assuming the system is in equilibrium, determine the range of possible values of $m$.

(b)[5]

It is now given that $m = 12$ and the particles are released from rest with the string taut. Use an energy method to determine the speed of the particles once each has moved $0.6$ m. You may assume that this happens before $A$ reaches the pulley or $B$ reaches the ground.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate identification $T=mg$ or $T-mg=0$.

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