| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics A AS (Further Mechanics A AS) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find final speed |
| Difficulty | Moderate -0.3 This is a straightforward multi-part momentum conservation problem with clear setup and standard techniques. Part (a) uses basic impulse-momentum theorem, part (b) applies conservation of momentum with relative velocity (though labeled 'show that'), and part (c) requires calculating kinetic energies. While it involves multiple steps and careful bookkeeping of masses, it requires no novel insight—just systematic application of standard A-level mechanics formulas. Slightly easier than average due to its structured, guided nature. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (a) | (i) |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) | Let the final speed of the trolley be u m s-1. | |
| 320𝑢 = 1920u=6 | B1 | 3.3 |
| Answer | Marks |
|---|---|
| (b) | Let the speed of the trolley after the first firing be v ms-1 in |
| Answer | Marks |
|---|---|
| 5 ( v − 9 0 ) + 3 1 5 v = 1 9 2 0 | M1 |
| M1 | 3.3 |
| 3.4 | Attempt at COLM |
| Answer | Marks | Guidance |
|---|---|---|
| unless correctly justified | Using their u | |
| v = 7 .4 0 6 2 5 7 .4 1 | A1 | 2.2a |
| Answer | Marks |
|---|---|
| (c) | Let the speed of the trolley after the second firing be w ms-1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 1 0 w + 5 ( w + 9 0 ) = 3 1 5 7 .4 0 6 2 5 | M1 | 3.1b |
| Answer | Marks |
|---|---|
| without explanation | M0 if signs |
| Answer | Marks | Guidance |
|---|---|---|
| w = 5 .9 7 7 6 7 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| I n i t i a l K E 6 | M1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| which is a loss of 0.74%. | A1 cao | 1.1 |
| Answer | Marks |
|---|---|
| (d) | We require everything other than the cannon ball being fired |
| Answer | Marks | Guidance |
|---|---|---|
| OR There is likely to be some friction / air resistance | B1 | 3.5b |
| friction or air resistance, etc | Or other |
Question 7:
7 | (a) | (i) | 4804=1920 (Ns) | B1 | 1.1 | Condone missing / incorrect units.
[1]
(ii) | Let the final speed of the trolley be u m s-1.
320𝑢 = 1920u=6 | B1 | 3.3
[1]
(b) | Let the speed of the trolley after the first firing be v ms-1 in
the forwards direction.
5 ( v − 9 0 ) + 3 1 5 v = 1 9 2 0 | M1
M1 | 3.3
3.4 | Attempt at COLM
Correct equation, using expressions
in a single variable which differ by
90, or two variables with an
equation to indicate their difference
is 90.
M1M0A0 for 320v ˗ 5× 90=320× 6
unless correctly justified | Using their u
v = 7 .4 0 6 2 5 7 .4 1 | A1 | 2.2a | AG
[3]
(c) | Let the speed of the trolley after the second firing be w ms-1
in the forwards direction.
3 1 0 w + 5 ( w + 9 0 ) = 3 1 5 7 .4 0 6 2 5 | M1 | 3.1b | Correct equation(s)
Allow 315w + 5 × 90 = 315 × 7.41
without explanation | M0 if signs
wrong
w = 5 .9 7 7 6 7 | A1 | 1.1 | Value rounding to 5.98
F i n a l K E 5 .9 7 7 62 7 2
= ( = 0 .9 9 2 5 7 3 3 )
I n i t i a l K E 6 | M1 | 3.4 | For final KE (or change) divided by
initial KE (using their u = 6). Allow
wrong/different masses
which is a loss of 0.74%. | A1 cao | 1.1 | 0.6 - 1.0 and loss (by valid method)
[4]
(d) | We require everything other than the cannon ball being fired
to be modelled as a single particle, but, e.g. driver is likely to
shift about.
OR There is likely to be some friction / air resistance | B1 | 3.5b | Mention of particle model or
friction or air resistance, etc | Or other
suitable
answer.
[1]
PMT
Need to get in touch?
If you ever have any questions about OCR qualifications or services (including administration, logistics and teaching) please feel free to get in
touch with our customer support centre.
Call us on
01223 553998
Alternatively, you can email us on
support@ocr.org.uk
For more information visit
ocr.org.uk/qualifications/resource-finder
ocr.org.uk
Twitter/ocrexams
/ocrexams
/company/ocr
/ocrexams
OCR is part of Cambridge University Press & Assessment, a department of the University of Cambridge.
For staff training purposes and as part of our quality assurance programme your call may be recorded or monitored. © OCR
2022 Oxford Cambridge and RSA Examinations is a Company Limited by Guarantee. Registered in England. Registered office
The Triangle Building, Shaftesbury Road, Cambridge, CB2 8EA.
Registered company number 3484466. OCR is an exempt charity.
OCR operates academic and vocational qualifications regulated by Ofqual, Qualifications Wales and CCEA as listed in their
qualifications registers including A Levels, GCSEs, Cambridge Technicals and Cambridge Nationals.
OCR provides resources to help you deliver our qualifications. These resources do not represent any particular teaching method
we expect you to use. We update our resources regularly and aim to make sure content is accurate but please check the OCR
website so that you have the most up-to-date version. OCR cannot be held responsible for any errors or omissions in these
resources.
Though we make every effort to check our resources, there may be contradictions between published support and the
specification, so it is important that you always use information in the latest specification. We indicate any specification changes
within the document itself, change the version number and provide a summary of the changes. If you do notice a discrepancy
between the specification and a resource, please contact us.
Whether you already offer OCR qualifications, are new to OCR or are thinking about switching, you can request more
information using our Expression of Interest form.
Please get in touch if you want to discuss the accessibility of resources we offer to support you in delivering our qualifications.7 The diagram shows a cannon fixed to a trolley. The trolley runs on a smooth horizontal track.\\
\includegraphics[max width=\textwidth, alt={}, center]{d1ec7861-dc8b-450b-8e05-c70479ab0dc2-8_310_1086_296_520}
A driver boards the trolley with two cannon balls. The combined mass of the trolley, driver, cannon and cannon balls is 320 kg . Each cannon ball has a mass of 5 kg . Initially the trolley is at rest.
A force of 480 N acts on the trolley in the forward direction for 4 seconds.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the magnitude of the impulse of the force on the trolley.
\item Calculate the speed of the trolley after the force stops acting.
The driver now fires a cannon ball horizontally in the backward direction. The cannon ball and cannon separate at a rate of $90 \mathrm {~ms} ^ { - 1 }$.
\end{enumerate}\item Show that, after the firing of the cannon ball, the trolley moves with a speed of $7.41 \mathrm {~ms} ^ { - 1 }$, correct to $\mathbf { 3 }$ significant figures.
The driver now reverses the direction of the cannon and fires the second cannon ball horizontally in the forward direction. Again, the cannon ball and cannon separate at a rate of $90 \mathrm {~ms} ^ { - 1 }$.
\item Calculate the overall percentage change in the kinetic energy of the trolley (alone) from before the first cannon ball is fired to after the second is fired, giving your answer correct to $\mathbf { 2 }$ decimal places. You should make clear whether the change in kinetic energy is a gain or a loss.
\item Give a reason why one of the modelling assumptions that was required in answering parts (a), (b) and (c) may not have been appropriate.
\section*{END OF QUESTION PAPER}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics A AS 2022 Q7 [10]}}