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

Newton's laws of motion — practice question

Two particles, with masses $5\,\text{kg}$ and $10\,\text{kg}$, are joined by a light inextensible string passing over a fixed smooth pulley. The $5\,\text{kg}$ particle lies on a rough fixed slope inclined at an angle of $\alpha$ to the horizontal, where $\tan\alpha = \frac{3}{4}$. The $10\,\text{kg}$ particle hangs beneath the pulley (see diagram). The coefficient of friction between the slope and the $5\,\text{kg}$ particle is $\frac{1}{2}$. The particles are released from rest.
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Determine the acceleration of the particles and the tension in the string.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Normal reaction: $R = 5g\cos\alpha = 4g$, so the friction is $F = \mu R = 2g$

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