| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find mass |
| Difficulty | Moderate -0.8 This is a straightforward M1 momentum conservation problem requiring direct application of the principle with given values. Part (a) uses conservation of momentum with one unknown, part (b) applies impulse-momentum theorem. Both are standard textbook exercises with no problem-solving insight needed, making it easier than average A-level questions. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance Notes |
| \(0.9 \times 2 - 0.6v = 0 + 0.6 \times 2\) | M1 | Equation with all terms – condone "0" missing. Terms must be of the form \(mv\), but condone sign errors. Condone \(g\) present as a common factor. |
| (correct unsimplified equation) | A1 | Correct unsimplified equation |
| \(v = 1\) | A1 (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance Notes |
| \(I = 0.6(v+2) = 1.8\) N s or \(I = 0.9 \times 2 = 1.8\) N s | M1 | Change in momentum of \(A\) or of \(B\). Condone sign slips and negative answer. No \(g\). |
| \(1.8\) N s | A1 (2) | 1.8 only (or exact equivalent). From correct work only. |
# Question 1:
## Part (a)
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $0.9 \times 2 - 0.6v = 0 + 0.6 \times 2$ | M1 | Equation with all terms – condone "0" missing. Terms must be of the form $mv$, but condone sign errors. Condone $g$ present as a common factor. |
| (correct unsimplified equation) | A1 | Correct unsimplified equation |
| $v = 1$ | A1 (3) | |
## Part (b)
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $I = 0.6(v+2) = 1.8$ N s or $I = 0.9 \times 2 = 1.8$ N s | M1 | Change in momentum of $A$ or of $B$. Condone sign slips and negative answer. No $g$. |
| $1.8$ N s | A1 (2) | 1.8 only (or exact equivalent). From correct work only. |
> **Note:** Watch out for fortuitous answers in (b); $v = 5$ from (a) used in (b) will score at most M1A0 in (b).
**Total: [5]**
---\begin{enumerate}
\item Two small smooth balls $A$ and $B$ have mass 0.6 kg and 0.9 kg respectively. They are moving in a straight line towards each other in opposite directions on a smooth horizontal floor and collide directly. Immediately before the collision the speed of $A$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of $B$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The speed of $A$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ immediately after the collision and $B$ is brought to rest by the collision.
\end{enumerate}
Find\\
(a) the value of $v$,\\
(b) the magnitude of the impulse exerted on $A$ by $B$ in the collision.\\
\hfill \mbox{\textit{Edexcel M1 2014 Q1 [5]}}