| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | String becomes taut problem |
| Difficulty | Moderate -0.3 This is a standard M1 string-becomes-taut problem requiring conservation of momentum and impulse-momentum theorem. The setup is straightforward with simple mass ratio (1:3), and both parts follow directly from textbook methods with minimal algebraic manipulation. Slightly easier than average due to its routine nature and clear structure. |
| 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 |
| CLM equation: \(mU = mS + 3mS\) | M1 | CLM equation with correct terms, condone sign errors and cancelled \(m\)'s or consistent extra \(g\)'s |
| \(S = \frac{1}{4}U\) or \(0.25U\) | A1 | cao (A0 if \(m\)'s not cancelled) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| For \(A\): \(\pm m(\frac{1}{4}U - U)\) | M1A1ft | M1: Impulse-momentum for \(A\) or \(B\), correct terms, condone sign errors; allow \(S\) for final speed but M0 if \(m\) omitted or extra \(g\) |
| \(\frac{3}{4}mU\) | A1 | Must be positive and a multiple of \(mU\) |
| Answer | Marks |
|---|---|
| For \(B\): \(\pm 3m\frac{1}{4}U\) | M1A1ft |
| \(\frac{3}{4}mU\) | A1 (3) |
# Question 1:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| CLM equation: $mU = mS + 3mS$ | M1 | CLM equation with correct terms, condone sign errors and cancelled $m$'s or consistent extra $g$'s |
| $S = \frac{1}{4}U$ or $0.25U$ | A1 | cao (A0 if $m$'s not cancelled) |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| For $A$: $\pm m(\frac{1}{4}U - U)$ | M1A1ft | M1: Impulse-momentum for $A$ or $B$, correct terms, condone sign errors; allow $S$ for final speed but M0 if $m$ omitted or extra $g$ |
| $\frac{3}{4}mU$ | A1 | Must be positive and a multiple of $mU$ |
**Alternative:**
| For $B$: $\pm 3m\frac{1}{4}U$ | M1A1ft | |
| $\frac{3}{4}mU$ | A1 (3) | |
---\begin{enumerate}
\item Two particles, $A$ and $B$, have masses $m$ and $3 m$ respectively. The particles are connected by a light inextensible string. Initially $A$ and $B$ are at rest on a smooth horizontal plane with the string slack.
\end{enumerate}
Particle $A$ is then projected along the plane away from $B$ with speed $U$.\\
Given that the common speed of the particles immediately after the string becomes taut is $S$\\
(a) find $S$ in terms of $U$.\\
(b) Find, in terms of $m$ and $U$, the magnitude of the impulse exerted on $A$ immediately after the string becomes taut.
\hfill \mbox{\textit{Edexcel M1 2024 Q1 [5]}}