| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| 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 Newton's experimental law (coefficient of restitution). Part (a) involves routine application of two equations to find mass ratios, part (b) is a standard modelling assumption recall, and part (c) requires setting up momentum conservation with an inequality. While multi-part with 11 marks total, all techniques are textbook-standard with no novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Momentum conserved: \(6x = \pm 2x + 3y\) where \(4x = 3y\) or \(8x = 3y\) | M1 A1 A1 | |
| \(x : y = 3 : 4\) or \(x : y = 3 : 8\) | M1 A1 A1 | |
| (b) Modelled as particles | B1 | |
| (c) \(2x - ky = vx\) where \(v < 0\), \(X\) moving towards \(Y\), so \(x : y = 3 : 4\) | M1 A1 | |
| Hence \(2 - \frac{4}{3}k < 0\) where \(k > 1.5\) | M1 A1 | Total: 11 marks |
**(a)** Momentum conserved: $6x = \pm 2x + 3y$ where $4x = 3y$ or $8x = 3y$ | M1 A1 A1 |
$x : y = 3 : 4$ or $x : y = 3 : 8$ | M1 A1 A1 |
**(b)** Modelled as particles | B1 |
**(c)** $2x - ky = vx$ where $v < 0$, $X$ moving towards $Y$, so $x : y = 3 : 4$ | M1 A1 |
Hence $2 - \frac{4}{3}k < 0$ where $k > 1.5$ | M1 A1 | **Total: 11 marks**Two smooth spheres $X$ and $Y$, of masses $x$ kg and $y$ kg respectively, are free to move in a smooth straight groove in a horizontal table. $X$ is projected with speed $6$ ms$^{-1}$ towards $Y$, which is stationary. After the collision $X$ moves with speed $2$ ms$^{-1}$ and $Y$ moves with speed $3$ ms$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the two possible values of the ratio $x : y$. \hfill [6 marks]
\item State a modelling assumption that you have made concerning $X$ and $Y$. \hfill [1 mark]
\end{enumerate}
$Y$ now strikes a vertical barrier and rebounds along the groove with speed $k$ ms$^{-1}$, colliding again with $X$ which is still moving at $2$ ms$^{-1}$. Given that in this impact $Y$ is brought to rest and the direction of motion of $X$ is reversed,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item show that $k > 1.5$. \hfill [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [11]}}