| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward application of the cosine and sine rules to find a resultant force. It requires standard vector addition techniques taught early in M1 with no problem-solving insight needed—just direct application of formulae to given values. The 6 marks reflect routine working rather than conceptual difficulty. |
| Spec | 3.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Cos. rule on force \(\triangle\): \(R^2 = 16 + 36 - 48 \cos 140°\) | \(R = 9.42 \text{ N}\) | M1 A1 M1 A1 |
| (b) \(\sin \theta / 6 = \sin 140° / R\) | \(\sin \theta = 0.409\) | \(\theta = 24.2°\) |
(a) Cos. rule on force $\triangle$: $R^2 = 16 + 36 - 48 \cos 140°$ | $R = 9.42 \text{ N}$ | M1 A1 M1 A1
(b) $\sin \theta / 6 = \sin 140° / R$ | $\sin \theta = 0.409$ | $\theta = 24.2°$ | M1 A1 | **6 marks**Forces of magnitude 4 N and 6 N act in directions which make an angle of $40°$ with each other, as shown.
Calculate
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the resultant of the two forces, [4 marks]
\item the angle, in degrees, between the resultant and the 4 N force. [2 marks]
\end{enumerate}
\includegraphics{figure_1}
\hfill \mbox{\textit{Edexcel M1 Q2 [6]}}