Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A block of mass $12\,\text{kg}$ rests on a rough plane inclined at an angle $\alpha$ to the horizontal, where $\alpha = \tan^{-1}(0.5)$. A force of $X\,\text{N}$ acts on the block, directed straight up the plane. The coefficient of friction between the block and the plane is $\mu$.
(a)[6]
Take $\mu = 0.15$ and $X = 20$. Determine the time for the block to travel $2\,\text{m}$ down the plane from rest.
(b)[4]
Instead, take $\mu \ne 0.15$ and suppose that when $X = 10$, the block is just about to move down the plane. Determine the value of $\mu$ and the value of $X$ for which the block is just about to move up the plane.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve the weight to obtain the component $R=12g\cos(\tan^{-1}0.5)$.” …