| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Two-sphere oblique collision |
| Difficulty | Challenging +1.2 This is a multi-step mechanics problem requiring geometric analysis of sphere collision, resolution along the line of centres, application of Newton's experimental law with restitution, and projectile motion. Part (a) is straightforward geometry (1 mark). Part (b) requires careful component resolution, simultaneous equations from momentum and restitution, then 2D projectile analysis—standard Further Maths mechanics but with several connected steps requiring methodical application of principles rather than novel insight. |
| Spec | 3.02h Motion under gravity: vector form6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| 11 | (a) | r |
| Answer | Marks | Guidance |
|---|---|---|
| 2r | B1 | |
| [1] | 3.1b | AG – where r is the common radius of the spheres – |
| Answer | Marks |
|---|---|
| (b) | v +v =Ucos30 |
| Answer | Marks |
|---|---|
| 8g | M1* |
| Answer | Marks |
|---|---|
| [7] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | Use of conservation of linear momentum (parallel to |
Question 11:
11 | (a) | r
sinθ= ⇒θ=30
2r | B1
[1] | 3.1b | AG – where r is the common radius of the spheres –
1
as a minimum accept sinθ= ⇒θ=30
2
(b) | v +v =Ucos30
A B
1
v −v =− Ucos30
A B
2
3 3
v = U
B
8
1
0=(v cos30)t− gt2
B
2
9U
t=
8g | M1*
A1
M1*
A1
A1
M1dep*
A1
[7] | 3.3
1.1
3.3
1.1
1.1
3.1b
1.1 | Use of conservation of linear momentum (parallel to
the line of centres) – correct number of terms
(condone no masses present for this mark)
If no masses present, then do not award this mark (but
all later marks can be awarded)
Use of Newton’s experimental law (parallel to the
line of centres) – correct number of terms
Use of NEL must be consistent with CLM
Correct expression for the speed of B after impact
(accept equivalent in terms of sine or cosine)
Apply s=ut+ 1at2vertically with
2
s=0,u=v cos30 with their v , a=±gor other
B B
complete method for finding t
(e.g. −v cos30=v cos30−gt)
B B
oe exact expression\includegraphics{figure_11}
The diagram shows two small identical uniform smooth spheres, A and B, just before A collides with B. Sphere B is at rest on a horizontal table with its centre vertically above the edge of the table. Sphere A is projected vertically upwards so that, just before it collides with B, the speed of A is $U$ m s$^{-1}$ and it is in contact with the vertical side of the table. The point of contact of A with the vertical side of the table and the centres of the spheres are in the same vertical plane.
\begin{enumerate}[label=(\alph*)]
\item Show that on impact the line of centres makes an angle of 30° with the vertical. [1]
\end{enumerate}
The coefficient of restitution between A and B is $\frac{1}{2}$. After the impact B moves freely under gravity.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine, in terms of $U$ and $g$, the time taken for B to first return to the table. [7]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2022 Q11 [8]}}