| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2020 |
| Session | October |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Particle on inclined plane - force parallel to slope |
| Difficulty | Easy -1.2 This is a straightforward mechanics question testing standard equilibrium on an inclined plane. Parts (a) and (b) involve routine resolution of forces (R = mg cos α and F = mg sin α leading to μ = tan α), which are textbook exercises. Parts (c) and (d) require only qualitative reasoning about limiting friction with no calculations. The question is easier than average A-level as it's highly structured with standard methods and minimal problem-solving required. |
| Spec | 3.03t 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 | Mark | Guidance |
| Resolve perpendicular to the plane | M1 | Correct no. of terms, condone sin/cos confusion |
| \(R = mg\cos\alpha = \frac{4}{5}mg\) | A1 | cao with no wrong working seen. \(mg\cos 36.86\) is A0 |
| (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Resolve parallel to the plane or horizontally or vertically | M1 | Correct no. of terms, condone sin/cos confusion |
| \(F = mg\sin\alpha\) or \(R\sin\alpha = F\cos\alpha\) | A1 | Correct equation |
| Use \(F = \mu R\) and solve for \(\mu\) | M1 | Must use \(F = \mu R\) (not merely state it) to obtain numerical value for \(\mu\). This is an independent M mark. |
| \(\mu = \frac{3}{4}\)* | A1* | Given answer correctly obtained |
| (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| The forces acting on \(Q\) will still balance as the \(m\)'s cancel; friction will increase in the same proportion as the weight component/force down the plane; the force pulling the brick down the plane increases by the same amount as the friction | B1 | Must have the 3 underlined phrases/words oe. This mark can be scored if they do the calculation. |
| (1 mark) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Brick \(Q\) slides down the plane with constant speed | B1 | Must say constant speed |
| No resultant force down the plane (so no acceleration) oe | B1 | Any appropriate equivalent statement. These marks can be scored if they do the calculation. |
| (2 marks) |
# Question 1:
## Part 1(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Resolve perpendicular to the plane | M1 | Correct no. of terms, condone sin/cos confusion |
| $R = mg\cos\alpha = \frac{4}{5}mg$ | A1 | cao with no wrong working seen. $mg\cos 36.86$ is A0 |
| **(2 marks)** | | |
## Part 1(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Resolve parallel to the plane or horizontally or vertically | M1 | Correct no. of terms, condone sin/cos confusion |
| $F = mg\sin\alpha$ or $R\sin\alpha = F\cos\alpha$ | A1 | Correct equation |
| Use $F = \mu R$ and solve for $\mu$ | M1 | Must use $F = \mu R$ (not merely state it) to obtain numerical value for $\mu$. This is an independent M mark. |
| $\mu = \frac{3}{4}$* | A1* | Given answer correctly obtained |
| **(4 marks)** | | |
## Part 1(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| The forces acting on $Q$ will still balance as the $m$'s cancel; friction will increase in the same proportion as the weight component/force down the plane; the force pulling the brick down the plane increases by the same amount as the friction | B1 | Must have the 3 underlined phrases/words oe. This mark can be scored if they do the calculation. |
| **(1 mark)** | | |
## Part 1(d):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Brick $Q$ slides down the plane with **constant** speed | B1 | Must say **constant** speed |
| No resultant force down the plane (so no acceleration) oe | B1 | Any appropriate equivalent statement. These marks can be scored if they do the calculation. |
| **(2 marks)** | | |
**Total: 9 marks**\begin{enumerate}
\item A rough plane is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha = \frac { 3 } { 4 }$
\end{enumerate}
A brick $P$ of mass $m$ is placed on the plane.\\
The coefficient of friction between $P$ and the plane is $\mu$\\
Brick $P$ is in equilibrium and on the point of sliding down the plane.\\
Brick $P$ is modelled as a particle.\\
Using the model,\\
(a) find, in terms of $m$ and $g$, the magnitude of the normal reaction of the plane on brick $P$\\
(b) show that $\mu = \frac { 3 } { 4 }$
For parts (c) and (d), you are not required to do any further calculations.\\
Brick $P$ is now removed from the plane and a much heavier brick $Q$ is placed on the plane.
The coefficient of friction between $Q$ and the plane is also $\frac { 3 } { 4 }$\\
(c) Explain briefly why brick $Q$ will remain at rest on the plane.
Brick $Q$ is now projected with speed $0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ down a line of greatest slope of the plane.\\
Brick $Q$ is modelled as a particle.\\
Using the model,\\
(d) describe the motion of brick $Q$, giving a reason for your answer.
\hfill \mbox{\textit{Edexcel Paper 3 2020 Q1 [9]}}