| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Range of forces for equilibrium |
| Difficulty | Standard +0.3 This is a standard M1 mechanics question on limiting equilibrium on an inclined plane. It requires resolving forces perpendicular and parallel to the plane, applying F=μR, and considering two limiting cases. The steps are routine and well-practiced, with given trig values eliminating calculation difficulty. Slightly above average due to the two-case analysis in part (iii), but still a textbook exercise. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
1\\
\includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-2_200_537_269_804}
A box of weight 100 N rests in equilibrium on a plane inclined at an angle $\alpha$ to the horizontal. It is given that $\sin \alpha = 0.28$ and $\cos \alpha = 0.96$. A force of magnitude $P \mathrm {~N}$ acts on the box parallel to the plane in the upwards direction (see diagram). The coefficient of friction between the box and the plane is 0.25 .\\
(i) Find the magnitude of the normal force acting on the box.\\
(ii) Given that the equilibrium is limiting, show that the magnitude of the frictional force acting on the box is 24 N .\\
(iii) Find the value of $P$ for which the box is on the point of slipping
\begin{enumerate}[label=(\alph*)]
\item down the plane,
\item up the plane.
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2005 Q1 [6]}}