Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $P$ and $Q$, with masses $0.6\,\text{kg}$ and $0.4\,\text{kg}$ respectively, are attached to the two ends of a light inextensible string. The string passes over a small smooth pulley fixed at the top of a vertical cross-section of a triangular prism. The prism has its base on horizontal ground, and both sloping faces are smooth. Each sloping face is inclined at angle $\theta$ to the ground, where $\sin \theta = 0.8$. At the beginning, the particles are held stationary on the sloping faces, with the string taut (see diagram). They are then released and travel along lines of greatest slope.
(i)[5]
Calculate the tension in the string and the acceleration of the particles while they are moving.
(ii)[4]
Determine the elapsed time from release until $Q$ attains its maximum height above the ground, given that $P$ has speed $2\,\text{m s}^{-1}$ when it reaches the ground, and that on reaching the ground $P$ comes to rest and stays at rest.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to $P$ or $Q$, or $(M-m)g \times 0.8 = (M+m)a$” …