| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2023 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with two possible outcomes |
| Difficulty | Standard +0.3 This is a standard M1 collision problem requiring conservation of momentum and interpretation of given conditions. While it has a slight twist (two possible scenarios from the speed difference condition), the mathematical steps are routine: set up momentum equation, use the constraint about speed difference, solve simultaneous equations, then calculate impulse. Slightly above average due to the ambiguity requiring consideration of cases, but well within typical M1 scope. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(v\) and \(v+1\) OR \(w-1\) and \(w\) (speeds after collision) | B1 | speed of \(B = 1 +\) speed of \(A\). Must be seen before CLM equation. Algebraic not numerical quantities |
| \((3m \times 1.5) + (m \times -1.5) = 3mv + m(v+1)\) [Or \((3m \times 1.5)+(m \times -1.5) = 3m(w-1)+mw\)] | M1 A1 | M1: Dimensionally correct CLM equation, correct number of terms. Allow consistent extra \(g\)'s or cancelled \(m\)'s. Ignore sign errors. Allow 2 unknowns for speeds after. A1: Correct equation in 1 unknown |
| Speed of \(A = \frac{1}{2}\) (m s\(^{-1}\)) | A1 | |
| Speed of \(B = \frac{3}{2}\) (m s\(^{-1}\)) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| For \(B\): \(\pm m(1.5--1.5)\) OR For \(A\): \(\pm 3m(0.5-1.5)\) | M1 A1ft | M1: Dimensionally correct impulse-momentum equation using \(A\) or \(B\), correct number of terms. Condone sign errors but must be difference of momenta. M0 if \(g\) included. A1ft: Correct unsimplified equation, ft from (a) |
| \(3m\) (Ns) | A1 | cao (must be positive) |
# Question 2:
## Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $v$ and $v+1$ OR $w-1$ and $w$ (speeds after collision) | B1 | speed of $B = 1 +$ speed of $A$. Must be seen before CLM equation. Algebraic not numerical quantities |
| $(3m \times 1.5) + (m \times -1.5) = 3mv + m(v+1)$ [Or $(3m \times 1.5)+(m \times -1.5) = 3m(w-1)+mw$] | M1 A1 | M1: Dimensionally correct CLM equation, correct number of terms. Allow consistent extra $g$'s or cancelled $m$'s. Ignore sign errors. Allow 2 unknowns for speeds after. A1: Correct equation in 1 unknown |
| Speed of $A = \frac{1}{2}$ (m s$^{-1}$) | A1 | |
| Speed of $B = \frac{3}{2}$ (m s$^{-1}$) | A1 | |
## Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| For $B$: $\pm m(1.5--1.5)$ OR For $A$: $\pm 3m(0.5-1.5)$ | M1 A1ft | M1: Dimensionally correct impulse-momentum equation using $A$ or $B$, correct number of terms. Condone sign errors but must be difference of momenta. M0 if $g$ included. A1ft: Correct unsimplified equation, ft from (a) |
| $3m$ (Ns) | A1 | cao (must be positive) |
---2. Two particles, $A$ and $B$, are moving in a straight line in opposite directions towards each other on a smooth horizontal surface when they collide directly.
Particle $A$ has mass $3 m \mathrm {~kg}$ and particle $B$ has mass $m \mathrm {~kg}$.\\
Immediately before the collision, both particles have a speed of $1.5 \mathrm {~ms} ^ { - 1 }$\\
Immediately after the collision, the direction of motion of $A$ is unchanged and the difference between the speed of $A$ and speed of $B$ is $1 \mathrm {~ms} ^ { - 1 }$
\begin{enumerate}[label=(\alph*)]
\item Find (i) the speed of $A$ immediately after the collision,\\
(ii) the speed of $B$ immediately after the collision.
\item Find, in terms of $m$, the magnitude of the impulse exerted on $B$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2023 Q2 [8]}}