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 joined by a light inextensible string. Particle $A$ is supported on a smooth plane inclined at an angle of $\theta^\circ$ to the horizontal. The string goes over a small smooth pulley $P$ fixed at the top of the plane, and $B$ hangs freely $0.5\,\text{m}$ above horizontal ground (see diagram). The particles are released from rest with both parts of the string taut.
(i)[3]
Since the system is in equilibrium, determine $\theta$.
(ii(a))[4]
Now let $\theta = 20$. In the later motion, particle $A$ does not reach $P$ and $B$ stays at rest after reaching the ground. Determine the tension in the string and the acceleration of the system.
(ii(b))[2]
Determine the speed of $A$ at the instant $B$ reaches the ground.
(a)[4]
Determine the tension in the string and the acceleration of the system.
(b)[2]
Determine the speed of $A$ at the instant $B$ reaches the ground.
(c)[5]
Use an energy method to determine the total distance $A$ moves up the plane before it comes to instantaneous rest.
Worked solution & mark scheme
This 20-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By resolving the forces, obtain $T=4\sin\theta$ for particle $A$ and $T=2$ for particle $B$” …