| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Standard +0.3 This is a standard two-collision momentum problem requiring straightforward application of conservation of momentum. Part (a) is routine calculation with given rebound speed. Part (b) requires recognizing that the critical condition is when P and Q have equal velocities after Q's collision with R, which is a common textbook scenario. The problem involves multiple steps but uses only basic momentum principles without requiring novel insight or complex reasoning. |
| Spec | 6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| 3(a) | Use of conservation of momentum, 3 terms | M1 |
| 0.1×5+0=0.1×(−1 )+0.2×(±v ) | A1 | |
| v=3 m s–1 | A1 | A0 for v=−3 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(b) | 0.2×their 3+0=0.2×u+0.5V | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| u−1 | B1 | Allow u=−1. Allow equality for finding greatest value of V. |
| Answer | Marks | Guidance |
|---|---|---|
| Greatest V =1.6 | A1 FT | FT on their 3 from 3(a) if u=−1 used. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(a) ---
3(a) | Use of conservation of momentum, 3 terms | M1 | Correct dimensions
0.1×5+0=0.1×(−1 )+0.2×(±v ) | A1
v=3 m s–1 | A1 | A0 for v=−3
3
--- 3(b) ---
3(b) | 0.2×their 3+0=0.2×u+0.5V | M1 | Use of conservation of momentum, 3 terms, correct dimensions.
Allow u=0 used or if Q and R coalesce
u−1 | B1 | Allow u=−1. Allow equality for finding greatest value of V.
Condition for no collision with P, may be a statement.
Greatest V =1.6 | A1 FT | FT on their 3 from 3(a) if u=−1 used.
3
Question | Answer | Marks | GuidanceThree particles $P$, $Q$ and $R$, of masses 0.1 kg, 0.2 kg and 0.5 kg respectively, are at rest in a straight line on a smooth horizontal plane. Particle $P$ is projected towards $Q$ at a speed of $5 \text{ m s}^{-1}$. After $P$ and $Q$ collide, $P$ rebounds with speed $1 \text{ m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $Q$ immediately after the collision with $P$. [3]
\end{enumerate}
$Q$ now collides with $R$. Immediately after the collision with $Q$, $R$ begins to move with speed $V \text{ m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Given that there is no subsequent collision between $P$ and $Q$, find the greatest possible value of $V$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2021 Q3 [6]}}