| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| 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 equilibrium problem requiring students to sum forces in i and j components separately and solve two simultaneous linear equations. It's purely procedural with no conceptual difficulty or problem-solving insight needed—easier than average for M1. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \((15\mathbf{i} + \mathbf{j}) + (5q\mathbf{i} - p\mathbf{j}) + (-3p\mathbf{i} - q\mathbf{j}) = \mathbf{0}\) | M1 | Equating sum of three forces to zero (implied by subsequent working) |
| \(3p - 5q = 15\) and \(p + q = 1\) | M1, A1 | Second M1 for equating i and j components to give TWO equations in \(p\) and \(q\) only; A1 for two correct equations |
| \(p = 2.5\), \(q = -1.5\) | M1 A1 A1 | Third M1 for substitution/elimination to get equation in \(p\) only or \(q\) only; A1 each for correct values |
# Question 1:
| Working/Answer | Marks | Guidance |
|---|---|---|
| $(15\mathbf{i} + \mathbf{j}) + (5q\mathbf{i} - p\mathbf{j}) + (-3p\mathbf{i} - q\mathbf{j}) = \mathbf{0}$ | M1 | Equating sum of three forces to zero (implied by subsequent working) |
| $3p - 5q = 15$ and $p + q = 1$ | M1, A1 | Second M1 for equating **i** and **j** components to give TWO equations in $p$ and $q$ only; A1 for two correct equations |
| $p = 2.5$, $q = -1.5$ | M1 A1 A1 | Third M1 for substitution/elimination to get equation in $p$ only or $q$ only; A1 each for correct values |
---\begin{enumerate}
\item Three forces, $( 15 \mathbf { i } + \mathbf { j } ) \mathrm { N } , ( 5 q \mathbf { i } - p \mathbf { j } ) \mathrm { N }$ and $( - 3 p \mathbf { i } - q \mathbf { j } ) \mathrm { N }$, where $p$ and $q$ are constants, act on a particle. Given that the particle is in equilibrium, find the value of $p$ and the value of $q$.\\
(6)\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2017 Q1 [6]}}