OCR PURE — Question 8 3 marks

Exam BoardOCR
ModulePURE
Marks3
PaperDownload PDF ↗
TopicVectors Introduction & 2D
TypeForces in equilibrium (find unknowns)
DifficultyModerate -0.3 This is a straightforward equilibrium problem requiring students to set up two simultaneous equations by equating i and j components to zero, then solve for p and q. It's slightly easier than average as it involves only basic algebraic manipulation with no conceptual difficulty beyond understanding equilibrium means forces sum to zero.
Spec1.10a Vectors in 2D: i,j notation and column vectors3.03m Equilibrium: sum of resolved forces = 0
8 A particle is in equilibrium under the action of the following three forces: \(( 2 p \mathbf { i } - 4 \mathbf { j } ) N , ( - 3 q \mathbf { i } + 5 p \mathbf { j } ) N\) and \(( - 13 \mathbf { i } - 6 \mathbf { j } ) N\).
Find the values of p and q .
Question 8:
AnswerMarks Guidance
\(-4 + 5p - 6 = 0 \Rightarrow p = 2\)B1 1.1
\(2p - 3q - 13 = 0\) and \(p=2 \Rightarrow q = \ldots\)M1 1.1
\(q = -3\)A1 1.1
[3 marks]
## Question 8:

$-4 + 5p - 6 = 0 \Rightarrow p = 2$ | **B1** | 1.1 | Correct value $p=2$ stated

$2p - 3q - 13 = 0$ and $p=2 \Rightarrow q = \ldots$ | **M1** | 1.1 | Equating **i**-components to zero and using their numerical $p$ to find $q$

$q = -3$ | **A1** | 1.1 |

**[3 marks]**

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8 A particle is in equilibrium under the action of the following three forces:\\
$( 2 p \mathbf { i } - 4 \mathbf { j } ) N , ( - 3 q \mathbf { i } + 5 p \mathbf { j } ) N$ and $( - 13 \mathbf { i } - 6 \mathbf { j } ) N$.\\
Find the values of p and q .

\hfill \mbox{\textit{OCR PURE  Q8 [3]}}
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