| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.5 This is a straightforward M1 collision problem requiring conservation of momentum to find k, then impulse = change in momentum. Both parts use standard formulas with clear setup and minimal algebraic manipulation. Slightly easier than average due to the symmetric velocity changes making the algebra particularly clean. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(m \cdot 5u - kmu = -\frac{m \cdot 5u}{2} + \frac{km \cdot u}{2}\) | M1 A1 | M1 for attempt at CLM equation, correct no. of terms, dimensionally correct. Allow consistent extra g's and cancelled \(m\)'s and \(u\)'s and sign errors. A1 for correct equation with or without \(m\)'s and \(u\)'s |
| \(k = 5\) | A1 | Second A1 for \(k=5\). N.B. May find impulse on each particle and equate impulses. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| For \(P\): \(I = m\left(\frac{5u}{2} - {-5u}\right)\) OR For \(Q\): \(I = km\left(\frac{u}{2} - {-u}\right)\) | M1 A1 | M1 for attempt at impulse = difference in momenta for either particle (must consider one particle). M0 if g's included or \(m\) or \(u\) omitted. Allow \(\pm m(\frac{5}{2}u - 5u)\) or \(\pm km(\frac{1}{2}u - u)\) |
| \(= \frac{15mu}{2}\) | A1 | A1 for \(7.5mu\) oe cao (\(-7.5mu\) is A0). Allow change of sign at end to obtain magnitude |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $m \cdot 5u - kmu = -\frac{m \cdot 5u}{2} + \frac{km \cdot u}{2}$ | M1 A1 | M1 for attempt at CLM equation, correct no. of terms, dimensionally correct. Allow consistent extra g's and cancelled $m$'s and $u$'s and sign errors. A1 for correct equation with or without $m$'s and $u$'s |
| $k = 5$ | A1 | Second A1 for $k=5$. N.B. May find impulse on each particle and equate impulses. |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| For $P$: $I = m\left(\frac{5u}{2} - {-5u}\right)$ OR For $Q$: $I = km\left(\frac{u}{2} - {-u}\right)$ | M1 A1 | M1 for attempt at impulse = difference in momenta for either particle (must consider one particle). M0 if g's included or $m$ or $u$ omitted. Allow $\pm m(\frac{5}{2}u - 5u)$ or $\pm km(\frac{1}{2}u - u)$ |
| $= \frac{15mu}{2}$ | A1 | A1 for $7.5mu$ oe cao ($-7.5mu$ is A0). Allow change of sign at end to obtain magnitude |
---\begin{enumerate}
\item Particle $P$ of mass $m$ and particle $Q$ of mass $k m$ are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the speed of $P$ is $5 u$ and the speed of $Q$ is $u$. Immediately after the collision the speed of each particle is halved and the direction of motion of each particle is reversed.
\end{enumerate}
Find\\
(a) the value of $k$,\\
(b) the magnitude of the impulse exerted on $P$ by $Q$ in the collision.\\
\hfill \mbox{\textit{Edexcel M1 2015 Q1 [6]}}