Moderate -0.3 This is a straightforward multi-part mechanics question testing standard work-energy principles and friction on inclines. Part (a) involves direct application of KE/PE formulas and the work-energy principle with given values. Part (b)(i) is a standard limiting friction result, and (b)(ii) requires calculating work against gravity and friction—all routine M2 techniques with no novel problem-solving required. Slightly easier than average due to clear structure and standard methods.
A stone of mass 0.6 kg falls vertically 1.5 m from A to B against resistance. Its downward speeds at A and \(B\) are \(5.5 \mathrm {~ms} ^ { - 1 }\) and \(7.5 \mathrm {~ms} ^ { - 1 }\) respectively.
Calculate the change in kinetic energy and the change in gravitational potential energy of the stone as it falls from A to B .
Calculate the work done against resistance to the motion of the stone as it falls from A to B .
Assuming the resistive force is constant, calculate the power with which the resistive force is retarding the stone when it is at A .
A uniform plank is inclined at \(40 ^ { \circ }\) to the horizontal. A box of mass 0.8 kg is on the point of sliding down it. The coefficient of friction between the box and the plank is \(\mu\).
Show that \(\mu = \tan 40 ^ { \circ }\).
The plank is now inclined at \(20 ^ { \circ }\) to the horizontal.
Calculate the work done when the box is pushed 3 m up the plank, starting and finishing at rest.
1
\begin{enumerate}[label=(\alph*)]
\item A stone of mass 0.6 kg falls vertically 1.5 m from A to B against resistance. Its downward speeds at A and $B$ are $5.5 \mathrm {~ms} ^ { - 1 }$ and $7.5 \mathrm {~ms} ^ { - 1 }$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Calculate the change in kinetic energy and the change in gravitational potential energy of the stone as it falls from A to B .
\item Calculate the work done against resistance to the motion of the stone as it falls from A to B .
\item Assuming the resistive force is constant, calculate the power with which the resistive force is retarding the stone when it is at A .
\end{enumerate}\item A uniform plank is inclined at $40 ^ { \circ }$ to the horizontal. A box of mass 0.8 kg is on the point of sliding down it. The coefficient of friction between the box and the plank is $\mu$.
\begin{enumerate}[label=(\roman*)]
\item Show that $\mu = \tan 40 ^ { \circ }$.
The plank is now inclined at $20 ^ { \circ }$ to the horizontal.
\item Calculate the work done when the box is pushed 3 m up the plank, starting and finishing at rest.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI M2 2012 Q1 [18]}}