| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Minor (Further Mechanics Minor) |
| Year | 2023 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Standard +0.8 This is a multi-stage mechanics problem requiring conservation of momentum, coefficient of restitution, impulse calculations, and energy considerations across three distinct phases (collision, wall impact, friction). While the individual techniques are A-level standard, the problem requires careful tracking of velocities through multiple events and connecting friction work to kinetic energy loss, making it moderately challenging with extended reasoning. |
| Spec | 3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | Let the speed of P when it reaches B be u m s-1. |
| Frictional force = 23 0 .5 g | B1 | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| Or a = − 23 g , so 0 2 = u 2 − 2 23 g 0 .6 | M1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| COLM: 0 .5 6 = 0 .5 − 2 .8 + 2 v | M1 | 3.3 |
| u = 2 .8 and v = 2 .2 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| = 2 .2 +6 2 .8 | M1 | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| = 2 .2 +6 2 .8 = 56 ( = 0 .8 3 3 3 ) | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | 0 .5 ( 2 .8 − ( − 6 ) ) = 4 .4 N s | B1 |
| towards A. | B1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Let the coefficient of friction between Q and AB be . | |
| Speed of Q when it reaches B is 2.2 m s-1 | B1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| Or a=−g, so 0 2 2 .2 2 2 g 0 .3 = − | M1 | 3.1b |
| 11 24 17 = ( = 0 .8 2 3 1 2 9 ) | A1 | 1.1 |
Question 3:
3 | (a) | Let the speed of P when it reaches B be u m s-1.
Frictional force = 23 0 .5 g | B1 | 3.3
Either 12 0 .5 u 2 − 23 0 .5 g 0 .6 = 0
Or a = − 23 g , so 0 2 = u 2 − 2 23 g 0 .6 | M1 | 3.4 | If using WEP, both KE and WD
against friction terms need to be
present.
Let the speed of Q be v m s-1 after collision with P.
COLM: 0 .5 6 = 0 .5 − 2 .8 + 2 v | M1 | 3.3 | Three terms. Condone sign error.
u = 2 .8 and v = 2 .2 | A1 | 1.1 | or if both seen in (b) and (c)
Coefficient of restitution between P and Q
= 2 .2 +6 2 .8 | M1 | 3.3 | Attempt at v v . Allow sign
se p a p p
errors but not num/dem switch.
= 2 .2 +6 2 .8 = 56 ( = 0 .8 3 3 3 ) | A1 | 1.1
[6]
(b) | 0 .5 ( 2 .8 − ( − 6 ) ) = 4 .4 N s | B1 | 3.3 | Use “their” value for 𝑢
towards A. | B1 | 1.1 | oe eg ‘towards B’, ‘in the direction
CB’
[2]
(c) | Let the coefficient of friction between Q and AB be .
Speed of Q when it reaches B is 2.2 m s-1 | B1 | 3.4 | Use “their” value for 𝑣
122.22−2g0.3=0
Either
2
Or a=−g, so 0 2 2 .2 2 2 g 0 .3 = − | M1 | 3.1b
11 24 17 = ( = 0 .8 2 3 1 2 9 ) | A1 | 1.1 | cao
[3]3 The diagram shows two blocks P and Q of masses 0.5 kg and 2 kg respectively, on a horizontal surface. The points $\mathrm { A } , \mathrm { B }$ and C lie on the surface in a straight line. There is a wall at C . The surface between B and C is smooth, and the surface between A and B is rough, such that the coefficient of friction between P and AB is $\frac { 2 } { 3 }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{cad8805d-59f6-4ed2-81f4-9e8c749461f5-3_229_1271_1601_278}
P is projected with a speed of $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ directly towards Q , which is at rest. As a result of the collision between P and Q, P changes direction and subsequently comes to rest at A. You may assume that P only collides with Q once.
\begin{enumerate}[label=(\alph*)]
\item Determine the coefficient of restitution between P and Q .
\item Calculate the impulse exerted on P by Q during their collision.
After colliding with P , Q strikes the wall, which is perpendicular to the direction of the motion of Q , and comes to rest exactly halfway between A and B . The collision between Q and the wall is perfectly elastic.
\item Determine the coefficient of friction between Q and AB .
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2023 Q3 [11]}}