| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Three-dimensional force systems: finding resultant and couple |
| Difficulty | Standard +0.8 This M5 question requires systematic application of moment calculations with vector cross products, understanding of force-couple systems, and working with 3D vectors. While the individual steps are methodical (resultant force, moments about a point, finding F3 for equilibrium), the multi-stage nature, 3D geometry, and requirement to work with couples makes this moderately challenging. It's harder than typical M1/M2 mechanics but represents standard M5 material requiring careful bookkeeping rather than deep insight. |
| 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 $\mathbf{F}_1 = (3i + k)$ N and $\mathbf{F}_2 = (4i + j - k)$ N act on a rigid body. The force $\mathbf{F}_1$ acts at the point with position vector $(2i - j + 3k)$ m and the force $\mathbf{F}_2$ acts at the point with position vector $(-3i + 2k)$ m. The two forces are equivalent to a single force $\mathbf{R}$ acting at the point with position vector $(i + 2j + k)$ m together with a couple of moment $\mathbf{G}$.
Find,
\begin{enumerate}[label=(\alph*)]
\item $\mathbf{R}$,
[2]
\item $\mathbf{G}$.
[4]
\end{enumerate}
A third force $\mathbf{F}_3$ is now added to the system. The force $\mathbf{F}_3$ acts at the point with position vector $(2i - k)$ m and the three forces $\mathbf{F}_1$, $\mathbf{F}_2$ and $\mathbf{F}_3$ are equivalent to a couple.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the magnitude of the couple.
[6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q4 [12]}}