| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Minor (Further Mechanics Minor) |
| Year | 2020 |
| Session | November |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Challenging +1.2 This is a multi-part momentum/collision problem requiring systematic application of conservation of momentum, coefficient of restitution, and energy loss formulas. While it has 5 parts and requires careful algebraic manipulation, each step follows standard mechanics procedures without requiring novel insight. Part (b) requires proving an inequality condition, and part (e) involves kinematics after multiple collisions, elevating it slightly above average difficulty for A-level Further Maths mechanics. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| Answer | Marks |
|---|---|
| 6(a) | mu =−mv +3mv |
| Answer | Marks |
|---|---|
| A 3 | M1* |
| Answer | Marks |
|---|---|
| [5] | 3.3 |
| Answer | Marks |
|---|---|
| 2.2a | Conservation of linear momentum – |
| Answer | Marks |
|---|---|
| after collision | Correct initial speed u |
| Answer | Marks |
|---|---|
| 6(b) | v = 1( 1+e ) u |
| Answer | Marks |
|---|---|
| B A | B1 |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 2.2a | Correct expression for speed of B |
| Answer | Marks |
|---|---|
| insufficient | May be seen in (a) but |
| Answer | Marks | Guidance |
|---|---|---|
| 6(c) | Kinetic energy is likely to be lost during the collisions | |
| (for example, likely to be converted into heat or sound) | B1 | |
| [1] | 3.5b | Must mention kinetic energy lost or |
| Answer | Marks |
|---|---|
| 6(e) | x−2 2 x |
| Answer | Marks |
|---|---|
| x=32(m) | M1* |
| Answer | Marks |
|---|---|
| [3] | 3.1b |
| Answer | Marks |
|---|---|
| 2.2a | Equate times in terms of required |
Question 6:
--- 6(a) ---
6(a) | mu =−mv +3mv
A B
−v −v =−eu
A B
v = 1( 3e−1 ) u
A 4
v >0⇒e>1
A 3 | M1*
M1*
M1dep*
A1
A1
[5] | 3.3
3.3
3.4
1.1
2.2a | Conservation of linear momentum –
correct number of terms but allow
sign errors
Newton’s experimental law – correct
number of terms – must be consistent
with CLM
Solves both equations to find v
A
Correct expression for speed of A
after collision | Correct initial speed u
must be used
--- 6(b) ---
6(b) | v = 1( 1+e ) u
B 4
w = 1e(1+e)u
B 4
w −v = 1e(1+e)u−1(3e−1)u = 1(e−1)2 u
B A 4 4 4
w >v unless e=1
B A | B1
B1ft
M1
A1
[4] | 1.1
3.4
3.1b
2.2a | Correct expression for speed of B
after collision
Speed of B after collision with the
wall (follow through their v )
B
Correctly compares speed of A and B
after both collisions
AG checking case when e =1 is
insufficient | May be seen in (a) but
must be used in this part
--- 6(c) ---
6(c) | Kinetic energy is likely to be lost during the collisions
(for example, likely to be converted into heat or sound) | B1
[1] | 3.5b | Must mention kinetic energy lost or
energy converted to other forms.
--- 6(e) ---
6(e) | x−2 2 x
= +
v v w
A B B
x−2 2 x 24 18x
= + ⇒4 ( x−2 )= +
1u 5 u 5 u 5 5
4 12 18
x=32(m) | M1*
M1dep*
A1
[3] | 3.1b
3.4
2.2a | Equate times in terms of required
distance x
Substitutes their speeds (with their
value of e) and solve for their x
PPMMTT
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recorded or monitored6 Stones A and B have masses $m \mathrm {~kg}$ and $3 m \mathrm {~kg}$ respectively. They lie at rest on a large area of smooth horizontal ice and may move freely over the ice. Stone A is given a horizontal impulse of magnitude $m u \mathrm {~N} s$ towards B so that the stones collide directly. After the collision the direction of motion of A is reversed. The coefficient of restitution between A and B is denoted by $e$.
\begin{enumerate}[label=(\alph*)]
\item Find the range of possible values of $e$.
After the collision, B subsequently collides with a vertical smooth wall perpendicular to its path and rebounds. The coefficient of restitution between $B$ and the wall is the same as the coefficient of restitution between A and B .
\item Show that A and B will collide again unless the collision between B and the wall is perfectly elastic.
\item Explain why modelling the collision between B and the wall as perfectly elastic is possibly unrealistic.
\item Given that the kinetic energy lost in the first collision between A and B is $\frac { 5 } { 24 } m u ^ { 2 }$, determine the value of $e$.
\item Given that B was 2 metres from the wall when the stones first collided, determine the distance of the stones from the wall when they next collide.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2020 Q6 [17]}}