| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Standard +0.3 This is a standard multi-collision momentum problem requiring systematic application of conservation of momentum across three collisions. While it has multiple parts and requires careful bookkeeping of velocities, each step uses routine mechanics techniques without requiring novel insight or complex problem-solving strategies. The algebraic manipulation is straightforward, making it slightly easier than average. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form |
| Answer | Marks |
|---|---|
| 4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). |
| Answer | Marks | Guidance |
|---|---|---|
| 4(a) | 4×10[+0]=4×0.5v+2v | M1 |
| Answer | Marks |
|---|---|
| A B | A1 |
| Answer | Marks |
|---|---|
| 4(b) | Conservation of momentum B, C |
| 2×10[+0]=2×v+3v | M1 |
| v=4 | A1 |
| Answer | Marks |
|---|---|
| A B | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4(c) | Conservation of momentum A, B | M1 |
| Answer | Marks |
|---|---|
| 3 | A1 |
| Answer | Marks |
|---|---|
| 2 | M1 |
| Answer | Marks |
|---|---|
| 2 3 2 | A1 |
| Answer | Marks |
|---|---|
| 3 3 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 4:
4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
--- 4(a) ---
4(a) | 4×10[+0]=4×0.5v+2v | M1
v =5 and v =10
A B | A1
2
--- 4(b) ---
4(b) | Conservation of momentum B, C
2×10[+0]=2×v+3v | M1
v=4 | A1
v >v , hence another collision
A B | A1
3
--- 4(c) ---
4(c) | Conservation of momentum A, B | M1
14
4×their5+2×their4=4v+2v v= (ms −1)
3 | A1
1
KE initial = ×4×102
2 | M1
1 14 1
KE final = ×6×their( )2 + ×1×their122
2 3 2 | A1
412 188
Loss of KE = 200− =
3 3 | A1
5
Question | Answer | MarksSmall smooth spheres $A$ and $B$, of equal radii and of masses 4 kg and 2 kg respectively, lie on a smooth horizontal plane. Initially $B$ is at rest and $A$ is moving towards $B$ with speed $10 \text{ ms}^{-1}$. After the spheres collide $A$ continues to move in the same direction but with half the speed of $B$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $B$ after the collision. [2]
\end{enumerate}
A third small smooth sphere $C$, of mass 1 kg and with the same radius as $A$ and $B$, is at rest on the plane. $B$ now collides directly with $C$. After this collision $B$ continues to move in the same direction but with one third the speed of $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that there is another collision between $A$ and $B$. [3]
\item $A$ and $B$ coalesce during this collision.
Find the total loss of kinetic energy in the system due to the three collisions. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q4 [10]}}