| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Angle change from impulse |
| Difficulty | Standard +0.3 This is a standard M3 impulse-momentum vector problem requiring resolution of components and Pythagoras. Students must apply impulse-momentum principle in 2D and use the 90° deflection constraint, but the method is routine for this module with no novel insight required—slightly easier than average. |
| Spec | 6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| \((-)15\cos\alpha = (0-) 0.5\times22\) or \(15\sin\beta = 0.5\times22\) | M1 | For using \(I = \Delta(mv)\) in 'x' direction or for sketching \(\Delta\) reflecting \(I = m(v-u)\) |
| Impulse makes angle \(42.8°\) (0.748 rads) with negative x-axis | A1 | AEF, but angle must be clear |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| \(15\sin\alpha = 0.5v\) or \(15\cos\beta = 0.5v\) or \((0.5v)^2 = 15^2 - 11^2\) | M1 | For using \(I = \Delta(mv)\) in 'y' direction or using sketched \(\Delta\) |
| Correct explicit expression for \(v\) | A1 | |
| Speed is \(20.4 \text{ ms}^{-1}\) | A1 | |
| [3] |
**Part i**
$(-)15\cos\alpha = (0-) 0.5\times22$ or $15\sin\beta = 0.5\times22$ | M1 | For using $I = \Delta(mv)$ in 'x' direction or for sketching $\Delta$ reflecting $I = m(v-u)$
Impulse makes angle $42.8°$ (0.748 rads) with negative x-axis | A1 | AEF, but angle must be clear
| [3] |
**Part ii**
$15\sin\alpha = 0.5v$ or $15\cos\beta = 0.5v$ or $(0.5v)^2 = 15^2 - 11^2$ | M1 | For using $I = \Delta(mv)$ in 'y' direction or using sketched $\Delta$
Correct explicit expression for $v$ | A1 |
Speed is $20.4 \text{ ms}^{-1}$ | A1 |
| [3] |1\\
\includegraphics[max width=\textwidth, alt={}, center]{67af8d98-85af-42b1-9e7f-c6380a1f8a3f-2_476_583_258_781}
A ball of mass 0.5 kg is moving with speed $22 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a straight line when it is struck by a bat. The impulse exerted by the bat has magnitude 15 N s and the ball is deflected through an angle of $90 ^ { \circ }$ (see diagram). Find\\
(i) the direction of the impulse,\\
(ii) the speed of the ball immediately after it is struck.
\hfill \mbox{\textit{OCR M3 2011 Q1 [6]}}