Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Two particles $A$ and $B$ have masses $m$ kg and $km$ kg respectively, with $k > 1$. They are fastened to the two ends of a light inextensible string. The string passes over a fixed smooth pulley, and the particles hang vertically beneath it. At the start, both particles are $0.81$ m above horizontal ground (see diagram). The system is released from rest, and particle $B$ hits the ground $0.9$ s later. In the later motion, particle $A$ does not reach the pulley.
(i)[7]
Determine the value of $k$ and demonstrate that the tension in the string before $B$ reaches the ground is $12m$ N.
(ii)[4]
At the moment when $B$ reaches the ground, the string breaks. Show that the speed of $A$ when it reaches the ground is $5.97$ m s$^{-1}$, correct to $3$ significant figures, and determine how long it takes, after the string breaks, for $A$ to reach the ground.
(iii)[2]
Sketch a velocity-time graph for the motion of particle $A$ from the instant the system is released until $A$ reaches the ground.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $s=ut+\tfrac12at^2$, giving $0.81=\tfrac12 a\times0.9^2$” …