Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $A$ and $B$, with masses $0.4\,\text{kg}$ and $0.2\,\text{kg}$ respectively, are linked by a light inextensible string that goes over a fixed smooth pulley. Each particle is $0.5\,\text{m}$ above the ground. They hang vertically, as shown in the diagram. The particles are released from rest. In the motion that follows, $B$ does not reach the pulley and $A$ comes to rest once it reaches the ground.
(i)[4]
For the motion before $A$ reaches the ground, show that the magnitude of the acceleration of each particle is $\frac{10}{3}\,\text{m s}^{-2}$ and find the tension in the string.
(ii)[4]
Find the greatest height reached by $B$ above the ground.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law for particle $A$ or $B$ (or for the system) to obtain equations like $4 - T = 0.4a$ and $T - 2 = 0.2a$” …