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 joined by a light inextensible string of length $2.8\,\text{m}$. The string goes 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 $0.3$. Particle $A$ is released and the system starts to move.
(a(i))[7]
Determine the acceleration of the particles and show that $B$ has speed $3.95\,\text{m s}^{-1}$ immediately before it reaches the floor, correct to $3$ significant figures.
(a(ii))[4]
Assuming that $B$ stays on the floor, determine the speed with which $A$ reaches the pulley.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law on $A$ or $B$” …