Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
The diagram depicts a fixed block with a horizontal upper face and another face that is inclined at an angle of $\theta^\circ$ to the horizontal, where $\sin\theta = \frac{3}{5}$. Particle $A$ of mass $0.3\,\text{kg}$ is at rest on the horizontal face and is connected to one end of a light inextensible string. The string runs over a small smooth pulley $P$ fixed at the block’s edge. The other end is joined to particle $B$ of mass $1.5\,\text{kg}$, which is resting on the sloping face of the block. The system is released from rest with the string taut.
(i)[5]
With the block smooth, find the acceleration of particle $A$ and the tension in the string.
(ii)[9]
Now suppose instead that the block is rough. The coefficient of friction between $A$ and the block is $\mu$ and the coefficient of friction between $B$ and the block is also $\mu$. In the first $3$ seconds of the motion, $A$ does not reach $P$ and $B$ does not reach the bottom of the sloping surface. The speed of the particles after $3\,\text{s}$ is $5\,\text{m s}^{-1}$. Find the acceleration of particle $A$ and the value of $\mu$.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Newton’s second law applied to the bodies or the system” …