| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.8 This is a straightforward M1 collision question requiring direct application of conservation of momentum and the impulse-momentum theorem. All steps are routine: set up momentum equation with sign convention, solve for unknown velocity, then calculate impulse as change in momentum. No conceptual difficulty or problem-solving insight required beyond standard textbook methods. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((4 \times 2u) + (-3u \times 2) = 4v + (2 \times 2u)\) OR Equating impulses: \(2(2u - -3u) = 4(-v - -2u)\) | M1 | Dimensionally correct CLM equation or equating of impulses equation. Allow consistent extra \(g\)'s. Ignore sign errors. May be \(+v\) or \(-v\) |
| Correct unsimplified equation | A1 | Correct unsimplified equation |
| \(\frac{1}{2}u\) (\(\text{m s}^{-1}\)) | A1 | Cao. Must be positive |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| The direction of motion is reversed. | B1 | Accept *opposite direction*. Do not accept *changed* or *to the left* or *backwards, away from B*. N.B. Dependent on correctly obtaining \(\frac{1}{2}u\) or \(-\frac{1}{2}u\) in (a) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| For \(B\): \(I = \pm 2(2u - -3u)\) OR For \(A\): \(I = \pm 4\left(\frac{u}{2} - -2u\right)\) | M1 | Dimensionally correct impulse-momentum equation using \(A\) or \(B\). Condone sign errors with appropriate velocities. M0 if \(g\) is included |
| Correct unsimplified equation | A1 | Correct unsimplified equation |
| \(I = 10u\) Ns or \(10u\) kg m s\(^{-1}\) | A1 | Cao with units. Accept kg m/s |
# Question 1:
## Part 1(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(4 \times 2u) + (-3u \times 2) = 4v + (2 \times 2u)$ **OR** Equating impulses: $2(2u - -3u) = 4(-v - -2u)$ | M1 | Dimensionally correct CLM equation or equating of impulses equation. Allow consistent extra $g$'s. Ignore sign errors. May be $+v$ or $-v$ |
| Correct unsimplified equation | A1 | Correct unsimplified equation |
| $\frac{1}{2}u$ ($\text{m s}^{-1}$) | A1 | Cao. Must be **positive** |
## Part 1(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| The direction of motion is reversed. | B1 | Accept *opposite direction*. Do not accept *changed* or *to the left* or *backwards, away from B*. **N.B.** Dependent on correctly obtaining $\frac{1}{2}u$ or $-\frac{1}{2}u$ in (a) |
## Part 1(c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| For $B$: $I = \pm 2(2u - -3u)$ **OR** For $A$: $I = \pm 4\left(\frac{u}{2} - -2u\right)$ | M1 | Dimensionally correct impulse-momentum equation using $A$ or $B$. Condone sign errors with appropriate velocities. M0 if $g$ is included |
| Correct unsimplified equation | A1 | Correct unsimplified equation |
| $I = 10u$ Ns or $10u$ kg m s$^{-1}$ | A1 | Cao **with** units. Accept kg m/s |
---\begin{enumerate}
\item A particle $A$ has mass 4 kg and a particle $B$ has mass 2 kg .
\end{enumerate}
The particles move towards each other in opposite directions along the same straight line on a smooth horizontal table and collide directly.
Immediately before the collision, the speed of $A$ is $2 u \mathrm {~ms} ^ { - 1 }$ and the speed of $B$ is $3 u \mathrm {~ms} ^ { - 1 }$\\
Immediately after the collision, the speed of $B$ is $2 u \mathrm {~ms} ^ { - 1 }$\\
The direction of motion of $B$ is reversed by the collision.\\
(a) Find, in terms of $u$, the speed of $A$ immediately after the collision.\\
(b) State the direction of motion of $A$ immediately after the collision.\\
(c) Find, in terms of $u$, the magnitude of the impulse received by $B$ in the collision. State the units of your answer.
\section*{[In this question $\mathbf { i }$ and $\mathbf { j }$ are horizontal perpendicular unit vectors.]}
\hfill \mbox{\textit{Edexcel M1 2023 Q1 [7]}}