| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with vector velocities |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum in two dimensions with vector notation. Part (a) requires direct substitution into momentum equations (m₁u₁ + m₂u₂ = (m₁+m₂)v), and part (b) is a simple rearrangement. No problem-solving insight needed—purely routine mechanics calculation that any competent M1 student should handle quickly. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| \(12\begin{bmatrix}4\\7\end{bmatrix}+4\begin{bmatrix}2\\3\end{bmatrix}=16\mathbf{v}\) | M1, A1 | Three term momentum equation; Correct equation |
| \(\mathbf{v}=\frac{1}{16}\begin{bmatrix}56\\96\end{bmatrix}=\begin{bmatrix}3.5\\6.0\end{bmatrix} \text{ ms}^{-1}\) | m1, A1 (4) | Solving for \(\mathbf{v}\); Correct velocity |
| Answer | Marks | Guidance |
|---|---|---|
| \(12\begin{bmatrix}4\\7\end{bmatrix}+4\mathbf{u}=16\begin{bmatrix}1\\4\end{bmatrix}\) | M1, A1 | Three term momentum equation; Correct equation |
| \(\mathbf{u}=\frac{1}{4}\begin{bmatrix}-32\\-20\end{bmatrix}=\begin{bmatrix}-8\\-5\end{bmatrix} \text{ ms}^{-1}\) | A1 (3) | Correct velocity |
## Question 2:
### Part (a)
$12\begin{bmatrix}4\\7\end{bmatrix}+4\begin{bmatrix}2\\3\end{bmatrix}=16\mathbf{v}$ | M1, A1 | Three term momentum equation; Correct equation
$\mathbf{v}=\frac{1}{16}\begin{bmatrix}56\\96\end{bmatrix}=\begin{bmatrix}3.5\\6.0\end{bmatrix} \text{ ms}^{-1}$ | m1, A1 (4) | Solving for $\mathbf{v}$; Correct velocity
### Part (b)
$12\begin{bmatrix}4\\7\end{bmatrix}+4\mathbf{u}=16\begin{bmatrix}1\\4\end{bmatrix}$ | M1, A1 | Three term momentum equation; Correct equation
$\mathbf{u}=\frac{1}{4}\begin{bmatrix}-32\\-20\end{bmatrix}=\begin{bmatrix}-8\\-5\end{bmatrix} \text{ ms}^{-1}$ | A1 (3) | Correct velocity
---2 A particle, $A$, of mass 12 kg is moving on a smooth horizontal surface with velocity $\left[ \begin{array} { l } 4 \\ 7 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$. It then collides and coalesces with a second particle, $B$, of mass 4 kg .
\begin{enumerate}[label=(\alph*)]
\item If before the collision the velocity of $B$ was $\left[ \begin{array} { l } 2 \\ 3 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$, find the velocity of the combined particle after the collision.
\item If after the collision the velocity of the combined particle is $\left[ \begin{array} { l } 1 \\ 4 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$, find the velocity of $B$ before the collision.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2005 Q2 [7]}}