Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A block with mass $3\,\text{kg}$ starts from rest on a rough horizontal plane. A force of magnitude $6\,\text{N}$ acts on the block at an angle of $\theta$ above the horizontal, where $\cos\theta = \frac{24}{25}$. The force acts for $5\,\text{s}$, and during this interval the block travels $4.5\,\text{m}$.
(i)[4]
Determine the magnitude of the frictional force acting on the block.
(ii)[3]
Show that the coefficient of friction between the block and the plane is $0.165$, correct to $3$ significant figures.
(iii)[4]
After the block has travelled a distance of $4.5\,\text{m}$, the force of magnitude $6\,\text{N}$ is taken away and the block then slows to rest. Find the total time for which the block is moving.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply of $s = ut + \tfrac12at^2$ to determine $a$, leading to $4.5 = \tfrac12 a \times 5^2$” …