Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
The diagram depicts a semi-circular track $ABC$ of radius $1.8\,\text{m}$, fixed in a vertical plane. Points $A$ and $C$ are at the same horizontal level, while point $B$ is at the lowest part of the track. Section $AB$ is smooth, whereas section $BC$ is rough. A small block is released from rest at $A$.
(a)[2]
Show that the speed of the block at $B$ is equal to $6\,\text{m s}^{-1}$.
(b)[3]
The block first comes to instantaneous rest at a height of $1.2\,\text{m}$ above the level of $B$. The work done against the resistance force during the block's motion from $B$ to this point is $4.5\,\text{J}$. Find the mass of the block.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use conservation of energy, giving $mg\times1.8=\frac12 mv^2$” …