Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

A smooth inclined plane of length $2.5$ m has one end on the horizontal floor, while the other end is raised to a height of $0.7$ m above the floor. Particles $P$ and $Q$, with masses $0.5$ kg and $0.1$ kg respectively, are connected to the ends of a light inextensible string that passes over a small smooth pulley fixed at the top of the plane. Particle $Q$ is kept at rest on the floor directly below the pulley. The string is taut and $P$ is at rest on the plane (see diagram). $Q$ is released and starts to move vertically upwards towards the pulley, while $P$ moves down the plane.
(i)[5]

Find the tension in the string and the magnitude of the acceleration of the particles before $Q$ reaches the pulley.

(ii)[3]

Find the string length.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply Newton’s second law to either the particle or the system

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