Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A block $B$ with mass $4\,\text{kg}$ is driven upwards along the line of greatest slope on a smooth plane that is tilted at $30^\circ$ to the horizontal by a force applied to $B$, and this force acts in the same direction as the motion of $B$. The block goes through points $P$ and $Q$ with speeds $12\,\text{m s}^{-1}$ and $8\,\text{m s}^{-1}$, respectively. $P$ and $Q$ are $10\,\text{m}$ apart, with $P$ at a lower level than $Q$.
(a)[2]
Determine the loss in kinetic energy of the block as it travels from $P$ to $Q$.
(b)[3]
Hence determine the work carried out by the force pushing the block up the slope while the block travels from $P$ to $Q$.
(c)[4]
At the point where the block arrives at $Q$, the force pushing it up the slope is taken away. Determine how long it then takes the block to get back to $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The decrease in KE is $\tfrac12 \times 4 \times (12^2 - 8^2)$” …