| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2024 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find mass |
| Difficulty | Moderate -0.8 This is a straightforward M1 momentum conservation problem requiring only direct application of the conservation formula with one unknown. The setup is clear, requires simple algebraic manipulation to find x, and part (b) is a direct impulse calculation using I = mv - mu. Easier than average as it's purely procedural with no conceptual challenges. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| CLM: \((5\times3) - x^2 = (5\times1)+(x\times1.5)\) OR: \(5(-1--3) = x(1.5--x)\) | M1 A1 | Forms CLM equation or equates impulses, condone sign errors and extra \(g\)'s. A1 = correct unsimplified equation |
| \(x = 2.5\) | A1 | Correct answer. If \(-4\) is seen, must be rejected (ignore units) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(I = \pm5(1-3)\) or \(I = \pm2.5(1.5--2.5)\) \((I = \pm x(1.5--x))\) | M1 A1 | Impulse-momentum equation, dimensionally correct, correct no. of terms for \(A\) or \(B\). Condone sign errors but must be attempting a difference. M0 if \(g\) included. A1 = correct numerical expression |
| \(\ | I\ | = 10\) (Ns) |
## Question 2:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| CLM: $(5\times3) - x^2 = (5\times1)+(x\times1.5)$ **OR:** $5(-1--3) = x(1.5--x)$ | M1 A1 | Forms CLM equation or equates impulses, condone sign errors and extra $g$'s. A1 = correct unsimplified equation |
| $x = 2.5$ | A1 | Correct answer. If $-4$ is seen, must be rejected (ignore units) |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $I = \pm5(1-3)$ or $I = \pm2.5(1.5--2.5)$ $(I = \pm x(1.5--x))$ | M1 A1 | Impulse-momentum equation, dimensionally correct, correct no. of terms for $A$ or $B$. Condone sign errors but must be attempting a difference. M0 if $g$ included. A1 = correct numerical expression |
| $\|I\| = 10$ (Ns) | A1 | cao must be positive. Ignore missing or wrong units. A0 if both 10 and another answer given |
---2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-04_204_947_242_559}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows two particles, $A$ and $B$, moving in opposite directions on a smooth horizontal surface. Particle $A$ has mass 5 kg and particle $B$ has mass $x \mathrm {~kg}$.
The particles collide directly.\\
Immediately before the collision, the speed of $A$ is $3 \mathrm {~ms} ^ { - 1 }$ and the speed of $B$ is $x \mathrm {~ms} ^ { - 1 }$\\
Immediately after the collision, the speed of $A$ is $1 \mathrm {~ms} ^ { - 1 }$ and its direction of motion is unchanged.
Immediately after the collision, the speed of $B$ is $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $x$.
\item Find the magnitude of the impulse exerted on $A$ by $B$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2024 Q2 [6]}}