| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with two possible outcomes |
| Difficulty | Moderate -0.3 This is a standard M1 collision problem requiring conservation of momentum and impulse calculation. Part (a) is straightforward impulse = change in momentum. Part (b) requires considering two cases for P's direction after collision, leading to a quadratic or two linear equations. The 'two possible values' structure is typical for M1 and requires careful sign consideration but no novel insight—slightly easier than average due to clear setup and standard techniques. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\pm5m(3u-(-2u))\) | M1 | Use of \(I = m(v-u)\) seen or implied, with correct terms. Condone sign errors. M0 if \(g\) included |
| \(25mu\) | A1 | Must be positive |
| (2) | ||
| Use of CLM | M1 | Or equal and opposite impulses. Requires all terms dimensionally correct. Condone sign errors. |
| \(3mku-10mu = 3mu+15mu\) or \(3mku-10mu = -3mu+15mu\) | A1 | Correct unsimplified equation for either case. |
| \(\Rightarrow k = \frac{28}{3}\) or \(k = \frac{22}{3}\) | A1 | One correct value. Any equivalent form. Accept decimal to 1dp or better. |
| Equation for second value | M1 | Their equation from M1 above with the final direction of \(P\) reversed. |
| Second value correct. | A1 | Any equivalent form. Accept decimal to 1dp or better. |
| (5) [7] |
| **Answer/Working** | **Mark** | **Guidance** |
|---|---|---|
| $\pm5m(3u-(-2u))$ | M1 | Use of $I = m(v-u)$ seen or implied, with correct terms. Condone sign errors. M0 if $g$ included |
| $25mu$ | A1 | Must be positive |
| | | (2) |
| Use of CLM | M1 | Or equal and opposite impulses. Requires all terms dimensionally correct. Condone sign errors. |
| $3mku-10mu = 3mu+15mu$ or $3mku-10mu = -3mu+15mu$ | A1 | Correct unsimplified equation for either case. |
| $\Rightarrow k = \frac{28}{3}$ or $k = \frac{22}{3}$ | A1 | One correct value. Any equivalent form. Accept decimal to 1dp or better. |
| Equation for second value | M1 | Their equation from M1 above with the final direction of $P$ reversed. |
| Second value correct. | A1 | Any equivalent form. Accept decimal to 1dp or better. |
| | | (5) [7] |\begin{enumerate}
\item A particle $P$ has mass $3 m$ and a particle $Q$ has mass $5 m$. The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly.
\end{enumerate}
Immediately before the collision the speed of $P$ is $k u$, where $k$ is a constant, and the speed of $Q$ is $2 u$.
Immediately after the collision the speed of $P$ is $u$ and the speed of $Q$ is $3 u$.\\
The direction of motion of $Q$ is reversed by the collision.\\
(a) Find, in terms of $m$ and $u$, the magnitude of the impulse exerted on $Q$ by $P$ in the collision.\\
(b) Find the two possible values of $k$.\\
\includegraphics[max width=\textwidth, alt={}, center]{5a2cf693-d966-4787-8778-ecc8a79a6265-03_2647_1837_118_114}\\
\hfill \mbox{\textit{Edexcel M1 2021 Q1 [7]}}