| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Easy -1.3 This is a straightforward vector addition question requiring only basic component addition and then magnitude/angle calculation using Pythagoras and arctangent. It's a standard textbook exercise with no problem-solving insight needed, making it easier than average for A-level. |
| Spec | 3.03e Resolve forces: two dimensions3.03p Resultant forces: using vectors |
\includegraphics{figure_1}
Two horizontal forces $\mathbf{P}$ and $\mathbf{Q}$ act at the origin $O$ of rectangular coordinates $Oxy$ (see diagram). The components of $\mathbf{P}$ in the $x$- and $y$-directions are $14$ N and $5$ N respectively. The components of $\mathbf{Q}$ in the $x$- and $y$-directions are $-9$ N and $7$ N respectively.
\begin{enumerate}[label=(\roman*)]
\item Write down the components, in the $x$- and $y$-directions, of the resultant of $\mathbf{P}$ and $\mathbf{Q}$. [2]
\item Hence find the magnitude of this resultant, and the angle the resultant makes with the positive $x$-axis. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q1 [6]}}