| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| 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 M1 resolving forces question with given trigonometric values. Students simply resolve each force into components using the provided sin/cos values, sum them, and find the resultant magnitude using Pythagoras. No problem-solving insight required—pure mechanical application of standard techniques with arithmetic that works out cleanly (y-component = 0 by design). |
| Spec | 3.03e Resolve forces: two dimensions3.03p Resultant forces: using vectors |
\includegraphics{figure_2}
Three horizontal forces of magnitudes $15$ N, $11$ N and $13$ N act on a particle $P$ in the directions shown in the diagram. The angles $\alpha$ and $\beta$ are such that $\sin \alpha = 0.28$, $\cos \alpha = 0.96$, $\sin \beta = 0.8$ and $\cos \beta = 0.6$.
\begin{enumerate}[label=(\roman*)]
\item Show that the component, in the $y$-direction, of the resultant of the three forces is zero. [4]
\item Find the magnitude of the resultant of the three forces. [3]
\item State the direction of the resultant of the three forces. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q2 [8]}}