| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Coalescence collision |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum with given masses and velocities, followed by a direct impulse calculation using change in momentum. Both parts require only standard formula application with no problem-solving insight or geometric complexity—easier than average A-level mechanics questions. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(12MU - 2MU = 5MV\) | M1 A1 | M1 for attempt at CLM equation, correct no. of terms, dimensionally correct. Allow consistent extra g's and cancelled M's and sign errors. First A1 for a correct equation. |
| \(2U = V\) | A1 (3) | Second A1 for \(2U\) (-2U A0). N.B. Allow U's to be dropped or omitted in the equation if U is inserted in answer at the end (full marks can be scored). However, if U is not inserted then M0. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(I = 2M(V - {-U})\) OR \(I = 3M(-V - {-4U})\) | M1 A1 | M1 for attempt at impulse = difference in momenta, for either particle (must be considering *one* particle). M0 if g's included, mass omitted, or equation dimensionally incorrect. Allow \(\pm 2M(V-U)\) or \(\pm 3M(-V-4U)\) where V is their speed which does *not* need to be substituted. First A1 for \(\pm 2M(2U - {-U})\) or \(\pm 3M(-2U - {-4U})\) |
| \(= 6MU\) | A1 (3) Total: 6 | A1 for \(6MU\) cao (\(-6MU\) is A0). Allow change of sign at end to obtain magnitude. |
## Question 1:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $12MU - 2MU = 5MV$ | M1 A1 | M1 for attempt at CLM equation, correct no. of terms, dimensionally correct. Allow consistent extra g's and cancelled M's and sign errors. First A1 for a correct equation. |
| $2U = V$ | A1 (3) | Second A1 for $2U$ (-2U A0). N.B. Allow U's to be dropped or omitted in the equation if U is inserted in answer at the end (full marks can be scored). However, if U is not inserted then M0. |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $I = 2M(V - {-U})$ OR $I = 3M(-V - {-4U})$ | M1 A1 | M1 for attempt at impulse = difference in momenta, for either particle (must be considering *one* particle). M0 if g's included, mass omitted, or equation dimensionally incorrect. Allow $\pm 2M(V-U)$ or $\pm 3M(-V-4U)$ where V is their speed which does *not* need to be substituted. First A1 for $\pm 2M(2U - {-U})$ or $\pm 3M(-2U - {-4U})$ |
| $= 6MU$ | A1 (3) **Total: 6** | A1 for $6MU$ cao ($-6MU$ is A0). Allow change of sign at end to obtain magnitude. |\begin{enumerate}
\item A truck $P$ of mass $2 M$ is moving with speed $U$ on smooth straight horizontal rails. It collides directly with another truck $Q$ of mass $3 M$ which is moving with speed $4 U$ in the opposite direction on the same rails. The trucks join so that immediately after the collision they move together. By modelling the trucks as particles, find\\
(a) the speed of the trucks immediately after the collision,\\
(b) the magnitude of the impulse exerted on $P$ by $Q$ in the collision.\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2014 Q1 [6]}}