| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: resultant and acceleration |
| Difficulty | Moderate -0.3 This is a straightforward M1 mechanics question testing basic vector operations: adding vectors, finding magnitude using Pythagoras, finding direction using tan^(-1), and calculating moments. All parts use standard formulas with no problem-solving insight required, though part (c) requires recognizing that moment = force × perpendicular distance, making it slightly less routine than pure calculation. |
| Spec | 3.03a Force: vector nature and diagrams3.03p Resultant forces: using vectors3.04a Calculate moments: about a point |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\mathbf{R} = \mathbf{F} + \mathbf{G} = 9\mathbf{i} + 12\mathbf{j}\) | M1 A1 A1 | |
| \( | \mathbf{R} | = \sqrt{9^2 + 12^2} = 15 \text{ N}\) |
| (b) \(\tan^{-1}(4/3) = 53.1°\) | M1 A1 | |
| (c) \(OP = 5 \text{ cm}\) | M1 A1 A1 | |
| Moment \(= 5 \times 15 = 75 \text{ Ncm}\) or \(0.75 \text{ Nm}\) | ||
| Total: 8 marks |
(a) $\mathbf{R} = \mathbf{F} + \mathbf{G} = 9\mathbf{i} + 12\mathbf{j}$ | M1 A1 A1 |
| $|\mathbf{R}| = \sqrt{9^2 + 12^2} = 15 \text{ N}$ | |
(b) $\tan^{-1}(4/3) = 53.1°$ | M1 A1 |
(c) $OP = 5 \text{ cm}$ | M1 A1 A1 |
| Moment $= 5 \times 15 = 75 \text{ Ncm}$ or $0.75 \text{ Nm}$ | |
| | **Total: 8 marks**Two forces $\mathbf{F}$ and $\mathbf{G}$ are given by $\mathbf{F} = (6\mathbf{i} - 5\mathbf{j})$ N, $\mathbf{G} = (3\mathbf{i} + 17\mathbf{j})$ N, where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors in the $x$ and $y$ directions respectively and the unit of length on each axis is 1 cm.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of $\mathbf{R}$, the resultant of $\mathbf{F}$ and $\mathbf{G}$. [3 marks]
\item Find the angle between the direction of $\mathbf{R}$ and the positive $x$-axis. [2 marks]
\end{enumerate}
$\mathbf{R}$ acts through the point $P(-4, 3)$. $O$ is the origin $(0, 0)$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Use the fact that $OP$ is perpendicular to the line of action of $\mathbf{R}$ to calculate the moment of $\mathbf{R}$ about an axis through the origin and perpendicular to the $x$-$y$ plane. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [8]}}