| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Rough inclined plane work-energy |
| Difficulty | Standard +0.3 This is a straightforward M2 work-energy question requiring standard application of the work-energy principle and friction formula. Part (a) involves calculating PE loss, KE gain, and finding work against friction by subtraction. Part (b) requires resolving forces perpendicular to the plane and using W = Fd. Both parts follow textbook methods with no novel insight required, making it slightly easier than average. |
| Spec | 3.03v Motion on rough surface: including inclined planes6.02b Calculate work: constant force, resolved component6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Work done against friction \(=\) Loss in GPE \(-\) Gain in KE \(= 5 \times 9.8 \times 10\sin 25 - \frac{1}{2} \times 5 \times 7^2 = 84.58...\) | M1, A2 | Must use work-energy principle. Needs KE & GPE and no other terms. Condone sign errors. \(-1\) each error |
| \(= 85\) (J) \(\quad\) (84.6) | A1 | Max 3 s.f. Must be \(+\)ve. Accept as \(10F = 84.6\) or equiv. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(F = \mu R = \mu \times 5g\cos 25\) | M1, A1 | Resolve to find \(F_{\max}\). \(g\) missing is accuracy error. Correct unsimplified |
| Work done \(= 10F = 10\mu \times 5g\cos 25 =\) their 85 | M1, A1ft | Use of work done \(=\) force \(\times\) distance to form equation for \(\mu\). Correct unsimplified equation for their \(10F\) |
| \(\mu = 0.19\) | A1 | Accept 0.190 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(F = \mu R = \mu \times 5g\cos 25\) | M1, A1 | Resolve to find \(F_{\max}\). \(g\) missing is accuracy error. Correct unsimplified |
| \(v^2 = u^2 + 2as \rightarrow 49 = 20a \rightarrow a = \frac{49}{20}\) | M1 | Complete method to equation in \(\mu\) |
| \(\text{N2L} \rightarrow 5 \times \frac{49}{20} = 5g\sin 25 - \mu \times 5g\cos 25\) | A1 | Correct unsimplified equation |
| \(\mu = 0.19\) | A1 | Accept 0.190 |
## Question 8:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Work done against friction $=$ Loss in GPE $-$ Gain in KE $= 5 \times 9.8 \times 10\sin 25 - \frac{1}{2} \times 5 \times 7^2 = 84.58...$ | M1, A2 | Must use work-energy principle. Needs KE & GPE and no other terms. Condone sign errors. $-1$ each error |
| $= 85$ (J) $\quad$ (84.6) | A1 | Max 3 s.f. Must be $+$ve. Accept as $10F = 84.6$ or equiv. |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $F = \mu R = \mu \times 5g\cos 25$ | M1, A1 | Resolve to find $F_{\max}$. $g$ missing is accuracy error. Correct unsimplified |
| Work done $= 10F = 10\mu \times 5g\cos 25 =$ their 85 | M1, A1ft | Use of work done $=$ force $\times$ distance to form equation for $\mu$. Correct unsimplified equation for their $10F$ |
| $\mu = 0.19$ | A1 | Accept 0.190 |
**Alt (b):**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $F = \mu R = \mu \times 5g\cos 25$ | M1, A1 | Resolve to find $F_{\max}$. $g$ missing is accuracy error. Correct unsimplified |
| $v^2 = u^2 + 2as \rightarrow 49 = 20a \rightarrow a = \frac{49}{20}$ | M1 | Complete method to equation in $\mu$ |
| $\text{N2L} \rightarrow 5 \times \frac{49}{20} = 5g\sin 25 - \mu \times 5g\cos 25$ | A1 | Correct unsimplified equation |
| $\mu = 0.19$ | A1 | Accept 0.190 |
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There is no mark scheme content visible in these images to extract. Could you please check if the correct pages were uploaded? The mark scheme questions and answers don't appear to have loaded in these images.8. The points $A$ and $B$ are 10 m apart on a line of greatest slope of a fixed rough inclined plane, with $A$ above $B$. The plane is inclined at $25 ^ { \circ }$ to the horizontal. A particle $P$ of mass 5 kg is released from rest at $A$ and slides down the slope. As $P$ passes $B$, it is moving with speed $7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find, using the work-energy principle, the work done against friction as $P$ moves from $A$ to $B$.
\item Find the coefficient of friction between the particle and the plane.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2014 Q8 [9]}}