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

Newton's laws of motion — practice question

A light inextensible string carries a particle $A$ of mass $0.26\text{ kg}$ at one end and a particle $B$ of mass $0.54\text{ kg}$ at the other. Particle $A$ is kept at rest on a rough plane inclined at angle $\alpha$ to the horizontal, where $\sin\alpha = \frac{5}{13}$. The string is taut and runs parallel to a line of greatest slope on the plane. It passes over a small smooth pulley at the top of the plane. Particle $B$ hangs motionless vertically below the pulley. The coefficient of friction between $A$ and the plane is $0.2$. Particle $A$ is released, and the particles begin to move.
(i)[6]

Determine the magnitude of the acceleration of the particles and the tension in the string.

(ii)[2]

Particle $A$ reaches the pulley $0.4\text{ s}$ after it begins to move. Find the distance moved by each of the particles.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Obtains reaction force $R = 2.6(12 \div 13) = 2.4$.

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