| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2019 |
| Session | January |
| Marks | 6 |
| 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 problem requiring only direct application of conservation of momentum and the impulse-momentum theorem. The question provides all necessary information explicitly, involves simple algebraic manipulation with given masses and velocities, and follows a standard two-part structure typical of routine mechanics exercises. No novel insight or complex problem-solving is required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(6mu - 3mu = -2m \cdot \frac{3u}{2} + 3mv\) | M1 A1 | CLM with correct no. of terms; one unknown. Allow consistent extra \(g\)'s and/or cancelled \(m\)'s. Condone sign errors |
| \(v = 2u\) | A1 | Must be positive. If all terms same sign: M1A0A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(I = \pm 2m\left(\frac{3u}{2} - {-3u}\right)\) | M1 A1 | Dimensionally correct impulse-momentum equation with consistent use of \(2m\) or \(3m\). M0 if \(g\) included or \(m\) omitted |
| Magnitude \(= 9mu\) | A1 | Must be positive |
| OR: \(I = \pm 3m(2u - {-u})\) | M1 A1 | Mark actual equation, not formula. Some candidates use \(I = m(v+u)\) when direction reversed |
| Magnitude \(= 9mu\) | A1 | Must be positive |
# Question 1:
## Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $6mu - 3mu = -2m \cdot \frac{3u}{2} + 3mv$ | M1 A1 | CLM with correct no. of terms; one unknown. Allow consistent extra $g$'s and/or cancelled $m$'s. Condone sign errors |
| $v = 2u$ | A1 | Must be positive. If all terms same sign: M1A0A0 |
## Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $I = \pm 2m\left(\frac{3u}{2} - {-3u}\right)$ | M1 A1 | Dimensionally correct impulse-momentum equation with consistent use of $2m$ or $3m$. M0 if $g$ included or $m$ omitted |
| Magnitude $= 9mu$ | A1 | Must be positive |
| **OR:** $I = \pm 3m(2u - {-u})$ | M1 A1 | Mark actual equation, not formula. Some candidates use $I = m(v+u)$ when direction reversed |
| Magnitude $= 9mu$ | A1 | Must be positive |
---\begin{enumerate}
\item Two particles, $A$ and $B$, have masses $2 m$ and $3 m$ respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane when they collide directly. Immediately before they collide, the speed of $A$ is $3 u$ and the speed of $B$ is $u$. As a result of the collision, the speed of $A$ is halved and the direction of motion of each particle is reversed.\\
(i) Find the speed of $B$ immediately after the collision.\\
(ii) Find the magnitude of the impulse exerted on $A$ by $B$ in the collision.\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2019 Q1 [6]}}