Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A block of mass $3\text{ kg}$ is first at rest at the lower end $O$ of a rough plane inclined at angle $\alpha$ to the horizontal, with $\sin \alpha = 0.6$ and $\cos \alpha = 0.8$. A force of magnitude $35\text{ N}$ acts on the block at angle $\beta$ above the plane, where $\sin \beta = 0.28$ and $\cos \beta = 0.96$. The block begins to move up the line of greatest slope of the plane and reaches point $A$ with speed $4\text{ m s}^{-1}$. The distance $OA$ is $12.5\text{ m}$ (see diagram). When the block is at $A$, the force of magnitude $35\text{ N}$ stops acting.
(i)[4]

For the block’s motion from $O$ to $A$, determine the work done against the frictional force on the block.

(ii)[3]

Determine the coefficient of friction between the block and the plane.

(iii)[4]

Determine the distance the block moves up the plane after passing through $A$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $v^2 = u^2 + 2as$ to obtain $a = 0.64$

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