| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | 3D force systems: reduction to single force |
| Difficulty | Challenging +1.2 This is a Further Maths M5 question on vector moments and couples requiring systematic application of standard techniques: finding resultant force (straightforward vector addition) and then using moment equilibrium about O to find the couple. While it involves 3D vectors and multiple steps, the method is direct and well-practiced at this level, making it moderately above average difficulty. |
| Spec | 1.10g Problem solving with vectors: in geometry3.04a Calculate moments: about a point |
Two forces $\mathbf{F}_1$ and $\mathbf{F}_2$ and a couple $\mathbf{G}$ act on a rigid body. The force $\mathbf{F}_1 = (3\mathbf{i} + 4\mathbf{j})$ N acts through the point with position vector $2\mathbf{i}$ m relative to a fixed origin $O$. The force $\mathbf{F}_2 = (2\mathbf{i} - \mathbf{j} + \mathbf{k})$ N acts through the point with position vector $(\mathbf{i} + \mathbf{j})$ m relative to $O$. The forces and couple are equivalent to a single force $\mathbf{F}$ acting through $O$.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf{F}$. [2]
\item Find $\mathbf{G}$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q3 [7]}}