| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Coalescence collision |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum in 2D with coalescence. Students simply apply m₁v₁ + m₂v₂ = (m₁+m₂)v for each component, then calculate magnitude. It's a standard textbook exercise requiring only direct formula application with no problem-solving insight or geometric complexity. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors6.03a Linear momentum: p = mv6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum |
| Answer | Marks | Guidance |
|---|---|---|
| \(2\begin{bmatrix} 3 \\ -2 \end{bmatrix} + 3\begin{bmatrix} -4 \\ 1 \end{bmatrix} = 5\mathbf{v}\) | M1 | Three term vector equation, with a '+' sign, for conservation of momentum |
| A1 | Correct equation. Deduct this first A mark for use of \(mg\) | |
| \(\mathbf{v} = \frac{1}{5}\begin{bmatrix} -6 \\ -1 \end{bmatrix} = \begin{bmatrix} -1.2 \\ -0.2 \end{bmatrix}\) | A1 | Correct velocity |
| Total: 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = \sqrt{1.2^2 + 0.2^2} = 1.22 \text{ ms}^{-1}\) | M1 | Finding speed from their velocity in part (a) (Must include addition of two terms) |
| A1F | Correct speed from their velocity. Accept 1.21 | |
| Total: 2 marks |
**2(a)**
| $2\begin{bmatrix} 3 \\ -2 \end{bmatrix} + 3\begin{bmatrix} -4 \\ 1 \end{bmatrix} = 5\mathbf{v}$ | M1 | Three term vector equation, with a '+' sign, for conservation of momentum |
| | A1 | Correct equation. Deduct this first A mark for use of $mg$ |
| $\mathbf{v} = \frac{1}{5}\begin{bmatrix} -6 \\ -1 \end{bmatrix} = \begin{bmatrix} -1.2 \\ -0.2 \end{bmatrix}$ | A1 | Correct velocity |
| **Total: 3 marks** | | |
**2(b)**
| $v = \sqrt{1.2^2 + 0.2^2} = 1.22 \text{ ms}^{-1}$ | M1 | Finding speed from their velocity in part (a) (Must include addition of two terms) |
| | A1F | Correct speed from their velocity. Accept 1.21 |
| **Total: 2 marks** | | |2 Two particles, $A$ and $B$, are moving on a smooth horizontal surface. Particle $A$ has mass 2 kg and velocity $\left[ \begin{array} { r } 3 \\ - 2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$. Particle $B$ has mass 3 kg and velocity $\left[ \begin{array} { r } - 4 \\ 1 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$. The two particles collide, and they coalesce during the collision.
\begin{enumerate}[label=(\alph*)]
\item Find the velocity of the combined particles after the collision.
\item Find the speed of the combined particles after the collision.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2007 Q2 [5]}}