| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | String at angle to slope |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem on a slope with a force at an angle. It requires resolving forces parallel and perpendicular to the plane, applying F=μR for limiting friction, and solving simultaneous equations. The setup is straightforward with clearly given values, making it slightly easier than average but still requiring systematic application of mechanics principles. |
| Spec | 3.03e Resolve forces: two dimensions3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\mu R\) seen or implied | B1 | |
| \(R = 2g\cos 20° + 40\cos 60°\) | M1 A2 | Resolving perpendicular to plane; must use \(2g\) with \(20°\) or \(70°\) and \(40\) with \(30°\) or \(60°\) |
| \(F = 40\cos 30° - 2g\cos 70°\) | M1 A2 | Resolving parallel to plane; must use \(2g\) with \(20°\) or \(70°\) and \(40\) with \(30°\) or \(60°\) |
| \(\mu = \dfrac{40\cos 30° - 2g\cos 70°}{2g\cos 20° + 40\cos 60°}\) | M1 M1 | Independent M1 for eliminating \(R\); independent M1 for solving for \(\mu\) |
| \(= 0.73\) or \(0.727\) | A1 |
## Question 5:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\mu R$ seen or implied | B1 | |
| $R = 2g\cos 20° + 40\cos 60°$ | M1 A2 | Resolving perpendicular to plane; must use $2g$ with $20°$ or $70°$ and $40$ with $30°$ or $60°$ |
| $F = 40\cos 30° - 2g\cos 70°$ | M1 A2 | Resolving parallel to plane; must use $2g$ with $20°$ or $70°$ and $40$ with $30°$ or $60°$ |
| $\mu = \dfrac{40\cos 30° - 2g\cos 70°}{2g\cos 20° + 40\cos 60°}$ | M1 M1 | Independent M1 for eliminating $R$; independent M1 for solving for $\mu$ |
| $= 0.73$ or $0.727$ | A1 | |
---5.
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\caption{Figure 2}
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A particle $P$ of mass 2 kg is held at rest in equilibrium on a rough plane by a constant force of magnitude 40 N . The direction of the force is inclined to the plane at an angle of $30 ^ { \circ }$. The plane is inclined to the horizontal at an angle of $20 ^ { \circ }$, as shown in Figure 2. The line of action of the force lies in the vertical plane containing $P$ and a line of greatest slope of the plane. The coefficient of friction between $P$ and the plane is $\mu$.
Given that $P$ is on the point of sliding up the plane, find the value of $\mu$.\\
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\hfill \mbox{\textit{Edexcel M1 2016 Q5 [10]}}