| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Particle on inclined plane - force at angle to slope |
| Difficulty | Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions and application of F=μR at limiting equilibrium. While it involves multiple steps (finding sin/cos from tan, resolving perpendicular and parallel to plane, applying friction law), these are routine techniques practiced extensively in M1. The setup is conventional with no novel insight required, making it slightly easier than average for A-level. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks |
|---|---|
| \(F = \frac{1}{3}R\) | B1 |
| \((\uparrow) R\cos\alpha - F\sin\alpha = 0.4g\) | M1 A1 |
| \(R = \frac{5}{8}g = 6.53\) or 6.5 | M1 A1 |
| Answer | Marks |
|---|---|
| \((\rightarrow)P - F\cos\alpha - R\sin\alpha = 0\) | M1 A2 |
| \(P = \frac{20}{48}g = 5.66\) or 5.7 | M1 A1 |
## (a)
$F = \frac{1}{3}R$ | B1 |
$(\uparrow) R\cos\alpha - F\sin\alpha = 0.4g$ | M1 A1 |
$R = \frac{5}{8}g = 6.53$ or 6.5 | M1 A1 |
**Total: (5)**
## (b)
$(\rightarrow)P - F\cos\alpha - R\sin\alpha = 0$ | M1 A2 |
$P = \frac{20}{48}g = 5.66$ or 5.7 | M1 A1 |
**Total: (5) [10]**\includegraphics{figure_2}
A particle of mass 0.4 kg is held at rest on a fixed rough plane by a horizontal force of magnitude $P$ newtons. The force acts in the vertical plane containing the line of greatest slope of the inclined plane which passes through the particle. The plane is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha = \frac{3}{4}$, as shown in Figure 2.
The coefficient of friction between the particle and the plane is $\frac{1}{3}$.
Given that the particle is on the point of sliding up the plane, find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the normal reaction between the particle and the plane,
[5]
\item the value of $P$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q7 [10]}}