| Exam Board | AQA |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2016 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Collision with coalescing particles |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum for part (a) and impulse-momentum theorem for part (b). Both parts require only direct substitution into standard formulas with minimal problem-solving. The main challenge is unit conversion (grams to kg), but otherwise this is below average difficulty for A-level mechanics. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = 1.5(0) + 0.03(0) = 1.5(-v) + 0.03(400)\) leading to \(v = 8 \text{ (ms}^{-1})\) | M1 A1 | M1: Correct terms, allow sign errors. OE, Condone the omission of the zero terms. A1: CAO |
| Answer | Marks | Guidance |
|---|---|---|
| \(I = 1.5(8) - 1.5(0)\) leading to \(I = 12 \text{ (Ns)}\) | M1 A1 | M1: Seeing their \(v\) multiplied by 1.5 and condone the omission of the zero term. A1: CAO, must be positive. |
**(a)**
| $v = 1.5(0) + 0.03(0) = 1.5(-v) + 0.03(400)$ leading to $v = 8 \text{ (ms}^{-1})$ | M1 A1 | M1: Correct terms, allow sign errors. OE, Condone the omission of the zero terms. A1: CAO |
**(b)**
| $I = 1.5(8) - 1.5(0)$ leading to $I = 12 \text{ (Ns)}$ | M1 A1 | M1: Seeing their $v$ multiplied by 1.5 and condone the omission of the zero term. A1: CAO, must be positive. |
**Total: 4 marks**
---At a firing range, a man holds a gun and fires a bullet horizontally. The bullet is fired with a horizontal velocity of $400 \text{ m s}^{-1}$. The mass of the gun is $1.5$ kg and the mass of the bullet is $30$ grams.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of recoil of the gun. [2 marks]
\item Find the magnitude of the impulse exerted by the man on the gun in bringing the gun to rest after the bullet is fired. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M3 2016 Q1 [4]}}