| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2019 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Modelling assumptions and refinements |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring standard SUVAT equations and resolution of forces on an inclined plane. Part (a) uses basic kinematics with constant acceleration, (b) tests conceptual understanding of friction, (c) applies SUVAT in reverse, and (d) requires resolving forces with friction—all routine A-level mechanics techniques with no novel problem-solving required. Slightly easier than average due to clear structure and standard methods. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve down the plane: \(2g\sin 20° = 2a\) | M1 | N2L with no other forces with attempt to resolving weight. Allow sin/cos interchange for M mark |
| \(a = g\sin 20°\ [= 3.352]\) | A1 | Allow \(a = -g\sin 20°\) if positive direction up slope is clear |
| \(s = ut + \frac{1}{2}at^2\) with \(s=0.7\), \(u=1.4\) and their \(a\) | M1 | Using suvat equation(s) leading to equation for \(t\); allow sign errors |
| \(0.7 = 1.4t + \frac{1}{2}(g\sin 20°)t^2\) | A1 | Correct equation using their \(0.5a\); allow coefficient of \(t^2\) 1.7 or better |
| \((4.9\sin 20°)t^2 + 1.4t - 0.7 = 0\) | A1 | Cao. Must select correct root if two roots given |
| Time taken is \(0.352\) s | A1 | Solution BC is sufficient. Allow if positive root only seen |
| Answer | Marks | Guidance |
|---|---|---|
| Friction (and/or air resistance) would have the effect of slowing the particle so ignoring friction underestimates time | B1 | Needs to indicate why ignoring resistance produces an underestimate. eg "friction will slow it down" |
| Answer | Marks | Guidance |
|---|---|---|
| \(s=0.7\), \(u=1.4\), \(t=0.8 \Rightarrow 0.7 = 1.4\times0.8 + \frac{1}{2}a\times0.8^2\) | M1 | Use of suvat equation(s) to find \(a\); allow sign errors |
| \(a = \dfrac{0.7 - 1.12}{0.32} = -1.3125\) (\(-1.31\) to 3sf) | A1 | Allow \(a=1.3125\) if sign convention clear. eg both \(u\) and \(s\) negative |
| Answer | Marks | Guidance |
|---|---|---|
| N2L down the plane | M1 | All forces present and weight resolved; allow sin/cos interchange |
| \(2g\sin 20° - F = 2\times(-1.3125)\) | A1 | Fully correct equation; \(F\) need not be evaluated here |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve perpendicular to plane: \(R = 2g\cos 20°\) | M1, A1 | No extra forces; fully correct equation; \(R\) need not be evaluated here. Notice \(R\) may be found first. |
| Answer | Marks | Guidance |
|---|---|---|
| Use of \(F = \mu R\) | M1 | Allow for their \(F\) and \(R\) used |
| \(\mu = \dfrac{9.32859...}{18.4...} = 0.506\) (3sf) | A1 | Accept 0.506 or 0.507. Must be 3sf |
## Question 16:
**Part (a):**
Resolve down the plane: $2g\sin 20° = 2a$ | M1 | N2L with no other forces with attempt to resolving weight. Allow sin/cos interchange for M mark
$a = g\sin 20°\ [= 3.352]$ | A1 | Allow $a = -g\sin 20°$ if positive direction up slope is clear
$s = ut + \frac{1}{2}at^2$ with $s=0.7$, $u=1.4$ and their $a$ | M1 | Using suvat equation(s) leading to equation for $t$; allow sign errors
$0.7 = 1.4t + \frac{1}{2}(g\sin 20°)t^2$ | A1 | Correct equation using their $0.5a$; allow coefficient of $t^2$ 1.7 or better
$(4.9\sin 20°)t^2 + 1.4t - 0.7 = 0$ | A1 | Cao. Must select correct root if two roots given
Time taken is $0.352$ s | A1 | Solution BC is sufficient. Allow if positive root only seen
**Part (b):**
Friction (and/or air resistance) would have the effect of slowing the particle so ignoring friction underestimates time | B1 | Needs to indicate why ignoring resistance produces an underestimate. eg "friction will slow it down"
**Part (c):**
$s=0.7$, $u=1.4$, $t=0.8 \Rightarrow 0.7 = 1.4\times0.8 + \frac{1}{2}a\times0.8^2$ | M1 | Use of suvat equation(s) to find $a$; allow sign errors
$a = \dfrac{0.7 - 1.12}{0.32} = -1.3125$ ($-1.31$ to 3sf) | A1 | Allow $a=1.3125$ if sign convention clear. eg both $u$ and $s$ negative
**Part (d):**
N2L down the plane | M1 | All forces present and weight resolved; allow sin/cos interchange
$2g\sin 20° - F = 2\times(-1.3125)$ | A1 | Fully correct equation; $F$ need not be evaluated here
$(F = 9.32859...)$
Resolve perpendicular to plane: $R = 2g\cos 20°$ | M1, A1 | No extra forces; fully correct equation; $R$ need not be evaluated here. Notice $R$ may be found first.
$(R = 18.4...)$
Use of $F = \mu R$ | M1 | Allow for their $F$ and $R$ used
$\mu = \dfrac{9.32859...}{18.4...} = 0.506$ (3sf) | A1 | Accept 0.506 or 0.507. Must be 3sf
I don't see any mark scheme content in the image you've shared. The image only shows the back cover/contact page of an OCR exam document, which contains:
- OCR's postal address (The Triangle Building, Shaftesbury Road, Cambridge, CB2 8EA)
- Customer Contact Centre details
- Phone/fax numbers
- Website (www.ocr.org.uk)
- Standard legal/registration information
- Cambridge Assessment and UKAS logos
There are **no questions, answers, mark allocations, or marking guidance** present in this image to extract.
Could you please share the actual mark scheme pages? They would typically contain tables with question numbers, expected answers, mark codes (M1, A1, B1, etc.), and examiner guidance notes.
16 A particle of mass 2 kg slides down a plane inclined at $20 ^ { \circ }$ to the horizontal. The particle has an initial velocity of $1.4 \mathrm {~ms} ^ { - 1 }$ down the plane. Two models for the particle's motion are proposed.
In model A the plane is taken to be smooth.
\begin{enumerate}[label=(\alph*)]
\item Calculate the time that model A predicts for the particle to slide the first 0.7 m .
\item Explain why model A is likely to underestimate the time taken.
In model B the plane is taken to be rough, with a constant coefficient of friction between the particle and the plane.
\item Calculate the acceleration of the particle predicted by model B given that it takes 0.8 s to slide the first 0.7 m .
\item Find the coefficient of friction predicted by model B , giving your answer correct to 3 significant figures.
\section*{END OF QUESTION PAPER}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2019 Q16 [14]}}