Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A load is moved along a horizontal straight track from $A$ to $B$ by a force of magnitude $P\,\text{N}$ acting at $30^\circ$ above the horizontal. The distance $AB$ is $80\,\text{m}$. As the load travels from $A$ to the midpoint $M$ of $AB$, its speed stays constant at $1.2\,\text{m s}^{-1}$.
(i)[2]
For the part of the motion from $A$ to $M$, $P = 25$. Calculate the work done by the force as the load travels from $A$ to $M$.
(ii)[5]
The speed of the load rises from $1.2\,\text{m s}^{-1}$ as it moves from $M$ towards $B$. For the motion from $M$ to $B$ the value of $P$ is $50$ and the work done against resistance is the same as that for the motion from $A$ to $M$. The mass of the load is $35\,\text{kg}$. Find the gain in kinetic energy of the load as it moves from $M$ to $B$ and hence find the speed with which it reaches $B$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying $WD = Fd\cos\theta$ gives $WD = 25 \times 40\cos30^\circ$” …