| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Horizontal force on slope |
| Difficulty | Standard +0.3 This is a standard M1 statics problem requiring resolution of forces on an inclined plane with a vertical rope. Students must find sin α and cos α from tan α, resolve perpendicular and parallel to the plane, and apply F = μR. While it involves multiple steps and careful component resolution, it follows a well-practiced routine with no novel insight required, making it slightly easier than average. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks |
|---|---|
| \(T \sin \alpha + 65.8 = 50 g \sin \alpha\) | M1 A1 |
| \(T = 255 \text{ N or } 260 \text{ N}\) | DM1A1 (4) |
| Answer | Marks |
|---|---|
| \(65.8\cos \alpha = R\sin \alpha\) | M1 A1 |
| \(\mu = 65.8/R = \tan \alpha = 7/24, 0.29 \text{ or better}\) | M1 A1 (4) |
## Part (a)
$T \sin \alpha + 65.8 = 50 g \sin \alpha$ | M1 A1 |
$T = 255 \text{ N or } 260 \text{ N}$ | DM1A1 (4) |
## Part (b)
$65.8\cos \alpha = R\sin \alpha$ | M1 A1 |
$\mu = 65.8/R = \tan \alpha = 7/24, 0.29 \text{ or better}$ | M1 A1 (4) |
**Notes for Question 2(a):**
First M1 for resolving parallel to the plane (or an equation in $T$ only)
First A1 for a correct equation.
Second M1 dependent for producing a value for $T$.
Second A1 for 255 (N) or 260 (N).
**Notes for Question 2(b):**
First M1 for any equation containing $R$.
First A1 for a correct equation. (If equation includes a $T$ term, they must be using a correct value of $T$ to score this mark)
Second M1 for $(65.8/\text{their } R)$.
Second A1 for $7/24$, $0.29$ or better.
---\includegraphics{figure_1}
A block of mass 50 kg lies on a rough plane which is inclined to the horizontal at an angle $\alpha$, where $\tan\alpha = \frac{7}{24}$. The block is held at rest by a vertical rope, as shown in Figure 1, and is on the point of sliding down the plane. The block is modelled as a particle and the rope is modelled as a light inextensible string. Given that the friction force acting on the block has magnitude 65.8 N, find
\begin{enumerate}[label=(\alph*)]
\item the tension in the rope, [4]
\item the coefficient of friction between the block and the plane. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2015 Q2 [8]}}