Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Particles $A$ and $B$, with masses $0.2 \text{ kg}$ and $0.45 \text{ kg}$ respectively, are linked by a light inextensible string of length $2.8 \text{ m}$. The string runs over a small smooth pulley at the edge of a rough horizontal surface, which is $2 \text{ m}$ above the floor. Particle $A$ is kept in contact with the surface at a distance of $2.1 \text{ m}$ from the pulley, while particle $B$ hangs freely. The coefficient of friction between $A$ and the surface is $0.3$. When particle $A$ is released, the system starts to move.
(i)[7]
Find the acceleration of the particles and show that the speed of $B$ immediately before it hits the floor is $3.95 \text{ m s}^{-1}$, correct to $3$ significant figures.
(ii)[4]
Provided that $B$ stays on the floor, find the speed with which $A$ arrives at the pulley.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Newton’s second law is used for both masses or for the combined system” …