| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Relative velocity: find resultant velocity (magnitude and/or direction) |
| Difficulty | Moderate -0.5 This is a straightforward 2D vectors question involving relative velocity. Given the structure (parts i and ii asking for simple identifications like 'B' and 'v'), this appears to be a basic mechanics problem requiring standard application of relative velocity formulas without complex problem-solving. It's slightly easier than average A-level content due to its routine nature, but not trivial since it involves vector mechanics concepts. |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.8T = 260 \times (DG) \times \cos\theta\) | M1 | Moments about D |
| \(DG = 1.7/2, \theta = (30+D)\) | M1 | Both needed |
| Angle \(BDC = 28°\) | DA1 | \(D = 28.072..\) |
| \(0.8T = 260 \times (1.7/2) \times \cos58.07\) | A1ft | \(\text{flcv}(DG = 0.8, 1.5, 1.7, \theta = 30, 28)\) |
| \(T = 146 \text{ N}\) | AG | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Moment of weight | M1 | |
| \(=(260\cos30°) \times 0.75 - (260\sin30°) \times 0.4\) | DA1 | Difference of moments of perp components \((116.87...)\) |
| M1 | Moments about D | |
| \(0.8T = 116.87..\) | A1 | Needs no evaluation |
| \(T = 146 \text{ N}\) | AG | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(F_x = 146\cos30°\) | B1 | \(126.52..\) |
| \(R = 260 + 146\cos60°\) | B1 | \(333.04..\) |
| \(\mu = \frac{(146\cos30°)}{(260+146\sin30°)}\) | M1 | Denominator not 260 |
| \(\mu = 0.38(0)\) | A1 | [4] |
**(i)**
$0.8T = 260 \times (DG) \times \cos\theta$ | M1 | Moments about D
$DG = 1.7/2, \theta = (30+D)$ | M1 | Both needed
Angle $BDC = 28°$ | DA1 | $D = 28.072..$
$0.8T = 260 \times (1.7/2) \times \cos58.07$ | A1ft | $\text{flcv}(DG = 0.8, 1.5, 1.7, \theta = 30, 28)$
$T = 146 \text{ N}$ | AG | A1 | [5]
**OR**
Moment of weight | M1 |
$=(260\cos30°) \times 0.75 - (260\sin30°) \times 0.4$ | DA1 | Difference of moments of perp components $(116.87...)$
| M1 | Moments about D
$0.8T = 116.87..$ | A1 | Needs no evaluation
$T = 146 \text{ N}$ | AG | A1 |
**(ii)**
$F_x = 146\cos30°$ | B1 | $126.52..$
$R = 260 + 146\cos60°$ | B1 | $333.04..$
$\mu = \frac{(146\cos30°)}{(260+146\sin30°)}$ | M1 | Denominator not 260
$\mu = 0.38(0)$ | A1 | [4] | [9]\includegraphics{figure_6}
$E$ has velocity $\vec{v}$
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item $B$
\item $v$
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2013 Q6}}