Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
The figure gives the vertical cross-section of a surface. $A$, $B$ and $C$ are three points on the cross-section. $B$ is at a level $h\,\text{m}$ above $A$. $C$ is at a level $0.5\,\text{m}$ below $A$. A particle with mass $0.2\,\text{kg}$ is projected up the slope from $A$ with initial speed $5\,\text{m}\,\text{s}^{-1}$. As it moves from $A$ to $C$, the particle remains in contact with the surface.
(a)[3]
The particle arrives at $B$ with speed $3\,\text{m}\,\text{s}^{-1}$, and there is no resistance force. Determine $h$.
(b)[3]
A resistance force now acts, and the particle does $3.1\,\text{J}$ of work against the resistance force as it travels from $A$ to $C$. Find the speed of the particle when it reaches $C$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct kinetic energy expression, for example $\tfrac12 \times 0.2 \times 5^2$ or $\tfrac12 \times 0.2 \times 3^2$” …