| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: resultant and acceleration |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring vector addition and Newton's second law. Part (a) involves adding vectors and using the parallel condition (ratio of components), which is standard A-level technique. Part (b) applies F=ma with given magnitude. Both parts are routine applications with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.10d Vector operations: addition and scalar multiplication3.03d Newton's second law: 2D vectors3.03p Resultant forces: using vectors |
A particle $P$ of mass $m \text{kg}$ is moving on a smooth horizontal surface under the action of two constant horizontal forces $(-4\mathbf{i} + 2\mathbf{j}) \text{N}$ and $(a\mathbf{i} + b\mathbf{j}) \text{N}$. The resultant of these two forces is $\mathbf{R} \text{N}$. It is given that $\mathbf{R}$ acts in a direction which is parallel to the vector $-\mathbf{i} + 3\mathbf{j}$.
\begin{enumerate}[label=(\alph*)]
\item Show that $3a + b = 10$. [3]
\end{enumerate}
It is given that $a = 6$ and that $P$ moves with an acceleration of magnitude $5\sqrt{10} \text{ms}^{-2}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the value of $m$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2023 Q10 [7]}}