Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
The diagram depicts a particle of mass $5\text{ kg}$ resting on a rough horizontal table, with two light inextensible strings attached to it and passing over smooth pulleys fixed at the table’s edges. Particles of masses $4\text{ kg}$ and $6\text{ kg}$ hang freely from the two string ends. The particle of mass $6\text{ kg}$ is $0.5\text{ m}$ above the ground. The system is in limiting equilibrium.
(a)[2]
Show that the coefficient of friction between the $5\text{ kg}$ particle and the table has value $0.4$.
(b)[5]
The $6\text{ kg}$ particle is then substituted by a particle of mass $8\text{ kg}$ and the system is released from rest. Find the acceleration of the $4\text{ kg}$ particle and the tensions in the strings.
(c)[5]
In the following motion, the $8\,\text{kg}$ particle strikes the ground and does not bounce back. Find the time that passes after the $8\,\text{kg}$ particle hits the ground before the other two particles come to instantaneous rest. (You may assume that this happens before either particle reaches a pulley.)
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve the forces to determine $R$ and $F$: $R=5g,\ F=6g-4g$” …