| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: equilibrium (find unknowns) |
| Difficulty | Moderate -0.8 This is a straightforward M1 equilibrium question requiring only basic vector addition and standard trigonometry. Part (a) involves simple arithmetic to find p and q from equilibrium conditions, while parts (b) and (c) use Pythagoras and inverse tangent—all routine textbook exercises with no problem-solving insight needed. |
| Spec | 3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.03p Resultant forces: using vectors |
3. Three forces $\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }$ and $\mathbf { F } _ { 3 }$ acting on a particle $P$ are given by
$$\begin{aligned}
& \mathbf { F } _ { 1 } = ( 7 \mathbf { i } - 9 \mathbf { j } ) \mathrm { N } \\
& \mathbf { F } _ { 2 } = ( 5 \mathbf { i } + 6 \mathbf { j } ) \mathrm { N } \\
& \mathbf { F } _ { 3 } = ( p \mathbf { i } + q \mathbf { j } ) \mathrm { N }
\end{aligned}$$
where $p$ and $q$ are constants.\\
Given that $P$ is in equilibrium,
\begin{enumerate}[label=(\alph*)]
\item find the value of $p$ and the value of $q$.
The force $\mathbf { F } _ { 3 }$ is now removed. The resultant of $\mathbf { F } _ { 1 }$ and $\mathbf { F } _ { 2 }$ is $\mathbf { R }$. Find
\item the magnitude of $\mathbf { R }$,
\item the angle, to the nearest degree, that the direction of $\mathbf { R }$ makes with $\mathbf { j }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2012 Q3 [8]}}