Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Two rectangular boxes $A$ and $B$ have the same dimensions. They are initially stationary on a rough horizontal floor, with $A$ placed on top of $B$. Box $A$ has mass $200\,\text{kg}$ and box $B$ has mass $250\,\text{kg}$. A horizontal force of magnitude $P\,\text{N}$ acts on $B$ (see diagram). The boxes stay at rest when $P \le 3150$ and begin to move when $P > 3150$.
(i)[3]
Find the coefficient of friction for the contact between $B$ and the floor.
(ii)[3]
The coefficient of friction between the two boxes is $0.2$. Since $P > 3150$ and there is no relative slipping between the boxes, show that the acceleration of the boxes is at most $2\,\text{m s}^{-2}$.
(iii)[3]
Find the greatest possible value of $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Normal reaction has value $R = 4500\text{ N}$” …