| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | June |
| Marks | 8 |
| 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 equilibrium on a slope question with friction. Part (a) is straightforward resolution perpendicular to the plane. Parts (b) and (c) require understanding that friction can act in either direction (limiting equilibrium cases), which is a key M1 concept but well-practiced. The tan α = 3/4 setup is typical, and all three parts follow standard procedures with no novel insight required. Slightly easier than average due to clear structure and routine application of methods. |
| Spec | 3.03n Equilibrium in 2D: particle under forces3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(R = 10g\cos\alpha\) | M1 | Allow sin/cos confusion |
| \(= 78.4\) or \(78\) N | A1 | Allow \(8g\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(F = 0.5R\) | B1 | \(F = 0.5R\) seen anywhere |
| \(P = 10g\sin\alpha + F\) | M1 A1 | Correct number of terms, with \(10g\) resolved |
| \(= 98\) | A1 | Allow \(10g\). For inequality never becoming equation: Max M1A1A0 for \(P \leq 10g\sin\alpha + F\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P = 10g\sin\alpha - F\) | M1 | Correct number of terms, with \(10g\) resolved |
| \(= 19.6\) or \(20\) | A1 | Allow \(2g\). For inequality never becoming equation: Max M1A0 |
## Question 3:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $R = 10g\cos\alpha$ | M1 | Allow sin/cos confusion |
| $= 78.4$ or $78$ N | A1 | Allow $8g$ |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $F = 0.5R$ | B1 | $F = 0.5R$ seen anywhere |
| $P = 10g\sin\alpha + F$ | M1 A1 | Correct number of terms, with $10g$ resolved |
| $= 98$ | A1 | Allow $10g$. For inequality never becoming equation: Max M1A1A0 for $P \leq 10g\sin\alpha + F$ |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P = 10g\sin\alpha - F$ | M1 | Correct number of terms, with $10g$ resolved |
| $= 19.6$ or $20$ | A1 | Allow $2g$. For inequality never becoming equation: Max M1A0 |
---3.
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\caption{Figure 1}
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A particle of mass 10 kg is placed on a fixed rough inclined plane. The plane is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha = \frac { 3 } { 4 }$. The particle is held in equilibrium by a force of magnitude $P$ newtons, which acts up the plane, as shown in Figure 1. The line of action of the force lies in a vertical plane that contains a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is $\frac { 1 } { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the normal reaction between the particle and the plane.
\item Find the greatest possible value of $P$.
\item Find the least possible value of $P$.
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VIXV SIHIANI III IM IONOO & VIAV SIHI NI JYHAM ION OO & VI4V SIHI NI JLIYM ION OO \\
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\hfill \mbox{\textit{Edexcel M1 2020 Q3 [8]}}