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

Newton's laws of motion — practice question

Particles $A$ and $B$, whose masses are $2.4\,\text{kg}$ and $1.2\,\text{kg}$ respectively, are joined by a light inextensible string that passes over a fixed smooth pulley. $A$ is initially at a height of $2.1\,\text{m}$ above a horizontal plane and $B$ is $1.5\,\text{m}$ above the plane. The particles hang vertically and are released from rest. In the motion that follows, $A$ arrives at the plane and does not rebound, and $B$ does not reach the pulley.
(a)[4]

Determine the magnitude of the acceleration of the particles before $A$ reaches the plane, and verify that the tension in the string at that stage is $16\,\text{N}$.

(b)[3]

Calculate the greatest height reached by $B$ above the plane.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use Newton’s second law on at least one particle to set up equations such as $2.4g-T=2.4a$ or $T-1.2g=1.2a$.

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