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

Newton's laws of motion — practice question

Particles $A$ and $B$, with masses $0.2\,\text{kg}$ and $0.3\,\text{kg}$ respectively, are attached to the two ends of a light inextensible string. That string runs over a small fixed smooth pulley fixed to the lower end of a rough plane inclined at an angle $\theta$ to the horizontal, where $\sin\theta = 0.6$. Particle $A$ is on the plane, while particle $B$ hangs vertically below the pulley and is $0.25\,\text{m}$ above horizontal ground. The part of the string from $A$ to the pulley is parallel to a line of greatest slope of the plane (see diagram). The coefficient of friction between $A$ and the plane is $1.125$. Particle $A$ is released from rest.
(a)[7]

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

(b)[4]

When $B$ reaches the ground, it stops. Find the total distance travelled by $A$ down the plane from the instant it is released until it comes to rest. You may assume that $A$ does not reach the pulley.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: $R=0.2g\times0.8$

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