| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Angle change from impulse |
| Difficulty | Standard +0.8 This M3 impulse question requires vector resolution in 2D, application of impulse-momentum theorem, and solving simultaneous equations involving trigonometry. While the setup is standard, finding both the impulse direction and final speed from the deflection angle requires careful geometric reasoning and algebraic manipulation beyond routine mechanics problems. |
| Spec | 6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (implied method) | M1 | For using \(I = \Delta(mv)\) in the direction of the original motion (or equivalent from use of relevant vector diagram) |
| \(20\cos\theta = 0.4 \times 25\) | A1 | |
| Direction at angle \(120°\) to original motion | A1 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (implied method) | M1 | For using \(I = \Delta(mv)\) perpendicular to direction of original motion (or equivalent from use of relevant vector diagram) |
| \(20\sin 60° = 0.4v\) | A1ft | |
| Speed is \(43.3 \text{ ms}^{-1}\) | A1 | 3 |
# Question 1:
## Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| (implied method) | M1 | For using $I = \Delta(mv)$ in the direction of the original motion (or equivalent from use of relevant vector diagram) |
| $20\cos\theta = 0.4 \times 25$ | A1 | |
| Direction at angle $120°$ to original motion | A1 | 3 | Accept $\theta = 60°$ with $\theta$ correctly identified |
## Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| (implied method) | M1 | For using $I = \Delta(mv)$ perpendicular to direction of original motion (or equivalent from use of relevant vector diagram) |
| $20\sin 60° = 0.4v$ | A1ft | |
| Speed is $43.3 \text{ ms}^{-1}$ | A1 | 3 | |
---1 A ball of mass 0.4 kg is moving in a straight line, with speed $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, when it is struck by a bat. The bat exerts an impulse of magnitude 20 N s and the ball is deflected through an angle of $90 ^ { \circ }$. Calculate\\
(i) the direction of the impulse,\\
(ii) the speed of the ball immediately after it is struck.
\hfill \mbox{\textit{OCR M3 2006 Q1 [6]}}