| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics A AS (Further Mechanics A AS) |
| Year | 2024 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Three-particle sequential collisions |
| Difficulty | Standard +0.3 This is a standard sequential collision problem requiring systematic application of conservation of momentum and Newton's restitution formula across multiple collisions. Part (a) is trivial recall, (b) is routine calculation showing energy loss, (c) requires setting up inequalities for collision conditions but follows a predictable method, and (d) is standard modeling critique. The multi-step nature and inequality work in (c) elevate it slightly above average, but it remains a textbook-style question with no novel insights required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | Because e 1 . |
| [1] | 1.2 | Allow 𝑒 ≠ 1 Must refer to 1, e.g. ‘Because 𝑒 = 4’ is B0 |
| Answer | Marks |
|---|---|
| (b) | Let the velocities of A and B after the first collision be v and |
| Answer | Marks |
|---|---|
| 25 | M1 |
| Answer | Marks |
|---|---|
| [5] | 3.3 |
| Answer | Marks |
|---|---|
| 2.2a | COLM. Allow one error (e.g. sign) |
| Answer | Marks |
|---|---|
| (c) | Let the velocities of B and C after the second collision be w |
| Answer | Marks |
|---|---|
| 𝑢 > 9 | M1 |
| Answer | Marks |
|---|---|
| [6] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | Note 𝑤 = their 𝑣 may be used from the start |
| Answer | Marks | Guidance |
|---|---|---|
| cont | (d) | e.g. the model does not account for any possible air resistance |
| [1] | 3.5a | Or any other correct limitation, e.g. |
Question 4:
4 | (a) | Because e 1 . | B1
[1] | 1.2 | Allow 𝑒 ≠ 1 Must refer to 1, e.g. ‘Because 𝑒 = 4’ is B0
5
Ignore any further comments
(b) | Let the velocities of A and B after the first collision be v and
A
v (m s-1) towards C.
B
2 5 = 2 v + 4 v
A B
v −v = 45
B A 5
v = − 1 , v = 3
A B
KE before = 12 2 5 2 ( = 2 5 J)
KE after = 12 2 ( − 1 ) 2 + 12 4 ( 3 ) 2 ( = 1 9 J)
25−19
Percentage energy loss = ×100 = 24%
25 | M1
M1
A1
M1
A1
[5] | 3.3
3.3
1.1
1.1
2.2a | COLM. Allow one error (e.g. sign)
NEL; Allow one error, but not coefficient placed on
wrong side.
Attempt at KEs, before and at least one sphere after
(numerical)
AG Fully correct working
(c) | Let the velocities of B and C after the second collision be w
B
and w (m s-1) in direction AC.
C
4𝑤 +(1)𝑤 = 4(3)+1(−𝑢)
B C
2
𝑤 −𝑤 = (3+𝑢)
C B
3
2
4𝑤 + (3+𝑢)+𝑤 = 12−𝑢
B B
3
1
𝑤 = 2− 𝑢
B
3
For third collision to occur, we require 𝑤 < 𝑣
B A
1
2− 𝑢 < −1
3
𝑢 > 9 | M1
M1
A1 FT
M1
M1
A1
[6] | 3.3
3.3
1.1
3.4
2.2a
1.1 | Note 𝑤 = their 𝑣 may be used from the start
B A
COLM; Allow one error
NEL; Allow one error (e.g. 𝑣 = 12 used), but not
B
coefficient placed on wrong side.
Both equations correct (signs must be consistent)
FT from their 𝑣
B
Eliminating 𝑤 to obtain an equation involving w and u
C B
(or equation for u if 𝑤 = −1 has been substituted)
𝐵
Comparing their w with their 𝑣 Allow =
B A
Signs must be correct, e.g M0 for their 𝑤 < 1
B
Ignore any further comparisons
This M1 can be awarded earlier, for substituting
𝑤 = their 𝑣 into both equations
B A
Must be strict inequality. Allow statement in words.
4
cont | (d) | e.g. the model does not account for any possible air resistance | B1
[1] | 3.5a | Or any other correct limitation, e.g.
In reality the surface would not be smooth
Motion would not be in a perfect straight line4 Three spheres A, B, and C, of equal radius are in the same straight line on a smooth horizontal surface. The masses of $\mathrm { A } , \mathrm { B }$ and C are $2 \mathrm {~kg} , 4 \mathrm {~kg}$ and 1 kg respectively.
Initially the three spheres are at rest.\\
Spheres $A$ and $C$ are each given impulses so that $A$ moves towards $B$ with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and C moves towards B with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{a96a0ebe-8f4f-4d79-9d11-9d348ef72314-5_325_1591_603_239}
The coefficient of restitution between $A$ and $B$ is $\frac { 4 } { 5 }$.\\
It is given that the first collision occurs between A and B .
\begin{enumerate}[label=(\alph*)]
\item State how you can tell from the information given above that kinetic energy is lost when A collides with B .
\item Show that the combined kinetic energy of A and B decreases by $24 \%$ during their collision.
Sphere B next collides with C. The coefficient of restitution between B and C is $\frac { 2 } { 3 }$.
\item Given that a third collision occurs, determine the range of possible values for $u$.
\item State one limitation of the model used in this question.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics A AS 2024 Q4 [13]}}