| Exam Board | Edexcel |
|---|---|
| Module | FM1 (Further Mechanics 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion up rough slope |
| Difficulty | Standard +0.3 This is a straightforward Further Mechanics question requiring application of the work-energy principle to motion on a rough slope. While it's FM1 content (making it slightly harder than standard A-level), it's a standard textbook exercise with clear given values and a direct method. The work-energy approach simplifies what would otherwise be a SUVAT problem, and all necessary information is provided. Part (b) is a standard modelling critique requiring minimal insight. |
| Spec | 3.03v Motion on rough surface: including inclined planes6.02c Work by variable force: using integration6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(R = 5g\cos\alpha \left(= 5g \times \frac{4\sqrt{3}}{7} = 48.497...\right)\) | M1 | Condone sin/cos confusion |
| Force due to friction \(= \mu \times 5g\cos\alpha\) | M1 | Use of \(\mu\times\) their R |
| Work-Energy equation | M1 | Must use work-energy; requires all terms; condone sin/cos confusion, sign errors and their \(R\) |
| \(\frac{1}{2}\times 5\times 64 = 5\times 9.8\times 14\sin\alpha + 14\mu R\) | A1 | Correct in \(\theta\) and \(\mu R\) |
| \(\mu = 0.0913\) or \(0.091\) | A1 | Accept 0.0913 or 0.091 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Appropriate refinement, e.g. do not model the parcel as a particle and therefore take air resistance into account; take into account the dimensions/uniformity of the parcel | B1 |
## Question 2:
**Part (a):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $R = 5g\cos\alpha \left(= 5g \times \frac{4\sqrt{3}}{7} = 48.497...\right)$ | M1 | Condone sin/cos confusion |
| Force due to friction $= \mu \times 5g\cos\alpha$ | M1 | Use of $\mu\times$ their R |
| Work-Energy equation | M1 | Must use work-energy; requires all terms; condone sin/cos confusion, sign errors and their $R$ |
| $\frac{1}{2}\times 5\times 64 = 5\times 9.8\times 14\sin\alpha + 14\mu R$ | A1 | Correct in $\theta$ and $\mu R$ |
| $\mu = 0.0913$ or $0.091$ | A1 | Accept 0.0913 **or** 0.091 |
**Part (b):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Appropriate refinement, e.g. do not model the parcel as a particle and therefore take air resistance into account; take into account the dimensions/uniformity of the parcel | B1 | |
---\begin{enumerate}
\item A parcel of mass 5 kg is projected with speed $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ up a line of greatest slope of a fixed rough inclined ramp.\\
The ramp is inclined at angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 7 }$\\
The parcel is projected from the point $A$ on the ramp and comes to instantaneous rest at the point $B$ on the ramp, where $A B = 14 \mathrm {~m}$.
\end{enumerate}
The coefficient of friction between the parcel and the ramp is $\mu$.\\
In a model of the parcel's motion, the parcel is treated as a particle.\\
(a) Use the work-energy principle to find the value of $\mu$.\\
(b) Suggest one way in which the model could be refined to make it more realistic.
\hfill \mbox{\textit{Edexcel FM1 Q2 [6]}}