| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 5 |
| 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 vector addition problem requiring students to equate components and solve two simultaneous linear equations. It involves only basic algebraic manipulation with no conceptual difficulty beyond understanding that resultant = F₁ + F₂, making it easier than average for A-level. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| \((2pi - 3qj) + (5qi + 4pj) = 2i + 9j\) equating coefficients of \(i\) and \(j\) gives \(2p + 5q = 2\) and \(4p - 3q = 9\) | M1 | |
| solve simultaneously to give \(p = \frac{3}{2}\), \(q = -1\) | M1 A1 | (5) |
$(2pi - 3qj) + (5qi + 4pj) = 2i + 9j$ equating coefficients of $i$ and $j$ gives $2p + 5q = 2$ and $4p - 3q = 9$ | M1 |
solve simultaneously to give $p = \frac{3}{2}$, $q = -1$ | M1 A1 | (5)\begin{enumerate}
\item The resultant of two forces $\mathbf { F } _ { 1 }$ and $\mathbf { F } _ { 2 }$ is $( - 2 \mathbf { i } + 9 \mathbf { j } ) \mathrm { N }$.
\end{enumerate}
Given that $\mathbf { F } _ { \mathbf { 1 } } = ( 2 p \mathbf { i } - 3 q \mathbf { j } ) \mathrm { N }$ and $\mathbf { F } _ { \mathbf { 2 } } = ( 5 q \mathbf { i } + 4 p \mathbf { j } ) \mathrm { N }$, calculate the values of $p$ and $q$.\\
(5 marks)\\
\hfill \mbox{\textit{Edexcel M1 Q1 [5]}}