| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | 3D force systems: reduction to single force |
| Difficulty | Standard +0.8 This M5 question requires vector mechanics including resultant forces, moments, and line of action determination using cross products. Part (a)(ii) demands finding the line of action through moment equilibrium (8 marks total), and part (b) involves couple calculations. While systematic, it requires confident 3D vector manipulation and understanding of equivalent force systems—more demanding than typical A-level pure maths but standard for M5. |
| Spec | 1.10g Problem solving with vectors: in geometry3.04b Equilibrium: zero resultant moment and force4.04g Vector product: a x b perpendicular vector |
Two forces $\mathbf{F}_1 = (i + 2j + 3k)$ N and $\mathbf{F}_2 = (3i + j + 2k)$ N act on a rigid body. The force $\mathbf{F}_1$ acts through the point with position vector $(2i + k)$ m and the force $\mathbf{F}_2$ acts through the point with position vector $(j + 2k)$ m.
\begin{enumerate}[label=(\alph*)]
\item If the two forces are equivalent to a single force $\mathbf{R}$, find
\begin{enumerate}[label=(\roman*)]
\item $\mathbf{R}$,
[2]
\item a vector equation of the line of action of $\mathbf{R}$, in the form $\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}$.
[6]
\end{enumerate}
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item If the two forces are equivalent to a single force acting through the point with position vector $(i + 2j + k)$ m together with a couple of moment $\mathbf{G}$, find the magnitude of $\mathbf{G}$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q4 [13]}}