| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Resultant force on lamina |
| Difficulty | Standard +0.3 This is a standard M1 moments question requiring calculation of moments using position vectors and solving simultaneous equations. Part (a) is routine application of the moment formula (cross product). Part (b) involves setting up two moment equations and solving for two unknowns—straightforward but requires careful algebraic manipulation. Slightly above average due to the two-part setup and vector algebra, but still a typical textbook exercise. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) moments about \(O\) (anticlockwise +ve) = \(5(2) + 2(3)\) | M2 | |
| \(= 16 \text{ Nm anticlockwise}\) | A2 | |
| (b) resultant about \(O\) is zero \(\Rightarrow 4p + q = 16\) | M1 A1 | |
| resultant about \(A\) is 34 Ns \(\Rightarrow 6p + 4q = 34\) | M1 A1 | |
| solving simult. \(p = 3, q = 4\) | M1 A1 | (10) |
(a) moments about $O$ (anticlockwise +ve) = $5(2) + 2(3)$ | M2 |
$= 16 \text{ Nm anticlockwise}$ | A2 |
(b) resultant about $O$ is zero $\Rightarrow 4p + q = 16$ | M1 A1 |
resultant about $A$ is 34 Ns $\Rightarrow 6p + 4q = 34$ | M1 A1 |
solving simult. $p = 3, q = 4$ | M1 A1 | (10) |4. The force $\mathbf { F } _ { \mathbf { 1 } } = ( 5 \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }$ acts at the point $A$ on a lamina where the position vector of $A$, relative to a fixed origin $O$, is $( 3 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m }$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the magnitude and the sense of the moment of the force about $O$.
Another force $\mathbf { F } _ { 2 } = ( p \mathbf { i } + q \mathbf { j } )$, acts at the point $B$ with position vector ( ${ } ^ { - } \mathbf { i } + 4 \mathbf { j }$ ) m so that the resultant moment of the two forces, $\mathbf { F } _ { 1 }$ and $\mathbf { F } _ { 2 }$, about $O$ is zero.
Given also that the moment of $\mathbf { F } _ { 2 }$ about $A$ is 34 Ns in a clockwise sense,
\item find the values of $p$ and $q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [10]}}