| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Particle just remains at rest |
| Difficulty | Standard +0.3 This is a standard mechanics problem requiring resolution of forces on an inclined plane and application of F=ma. Part (a) involves routine calculation using given deceleration to find friction coefficient. Part (b) tests understanding of limiting friction for equilibrium. While it requires careful force analysis and comparison of forces, the techniques are standard A-level mechanics with no novel insight needed—slightly easier than average overall. |
| Spec | 3.03r Friction: concept and vector form3.03s Contact force components: normal and frictional3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = mg\cos\alpha\) | B1 | For \(R = mg\cos\alpha\) |
| Resolve parallel to the plane | M1 | For resolving parallel to the plane |
| \(-F - mg\sin\alpha = -0.8mg\) | A1 | For a correct equation |
| \(F = \mu R\) | M1 | For use of \(F = \mu R\) |
| Produce an equation in \(\mu\) only and solve for \(\mu\) | M1 | For eliminating \(F\) and \(R\) to give a value for \(\mu\) |
| \(\mu = \dfrac{1}{4}\) | A1 | For \(\mu = \dfrac{1}{4}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Compare \(\mu mg\cos\alpha\) with \(mg\sin\alpha\) | M1 | Comparing size of limiting friction with weight component down the plane |
| Deduce an appropriate conclusion | A1ft | For an appropriate conclusion from their values |
## Question 7:
### Part (a):
| $R = mg\cos\alpha$ | B1 | For $R = mg\cos\alpha$ |
| Resolve parallel to the plane | M1 | For resolving parallel to the plane |
| $-F - mg\sin\alpha = -0.8mg$ | A1 | For a correct equation |
| $F = \mu R$ | M1 | For use of $F = \mu R$ |
| Produce an equation in $\mu$ only and solve for $\mu$ | M1 | For eliminating $F$ and $R$ to give a value for $\mu$ |
| $\mu = \dfrac{1}{4}$ | A1 | For $\mu = \dfrac{1}{4}$ |
### Part (b):
| Compare $\mu mg\cos\alpha$ with $mg\sin\alpha$ | M1 | Comparing size of limiting friction with weight component down the plane |
| Deduce an appropriate conclusion | A1ft | For an appropriate conclusion from their values |
---\begin{enumerate}
\item A rough plane is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha = \frac { 3 } { 4 }$.
\end{enumerate}
A particle of mass $m$ is placed on the plane and then projected up a line of greatest slope of the plane.
The coefficient of friction between the particle and the plane is $\mu$.\\
The particle moves up the plane with a constant deceleration of $\frac { 4 } { 5 } \mathrm {~g}$.\\
(a) Find the value of $\mu$.
The particle comes to rest at the point $A$ on the plane.\\
(b) Determine whether the particle will remain at $A$, carefully justifying your answer.
\hfill \mbox{\textit{Edexcel Paper 3 Q7 [8]}}