OCR MEI Further Mechanics Major 2019 June — Question 1 5 marks

Exam BoardOCR MEI
ModuleFurther Mechanics Major (Further Mechanics Major)
Year2019
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeThree-dimensional force systems: finding resultant and couple
DifficultyStandard +0.3 This is a straightforward Further Mechanics question on couples requiring knowledge that forces must sum to zero for a couple, then calculating moment magnitude. The vector arithmetic is simple, and the method is standard textbook application with no novel problem-solving required. Being Further Maths raises baseline difficulty slightly, but this remains an accessible introductory question on the topic.
Spec3.04a Calculate moments: about a point6.05e Radial/tangential acceleration
Three forces represented by the vectors \(-4\mathbf{i} + \mathbf{j} + 2\mathbf{j}\) and \(k\mathbf{i} - 2\mathbf{j}\) act at the points with coordinates \((0, 0)\), \((3, 0)\) and \((0, 4)\) respectively.
  1. Given that the three forces form a couple, find the value of \(k\). [2]
  2. Find the magnitude and direction of the couple. [3]
Question 1:
AnswerMarks Guidance
1(a) 41k0
k3M1
A1
AnswerMarks
[2]1.1a
1.1Consideration of i-component (allow
sign errors)
AnswerMarks
Sight of 3 scores both marksk3 with no working
scores no marks
AnswerMarks Guidance
1(b) e.g. taking moments about O: 4(k) – 3(2)
6
AnswerMarks
clockwiseM1
A1
B1
AnswerMarks
[3]1.1a
1.1
AnswerMarks
2.5Taking moments correctly about any
point with correct number of terms
oe (could be seen on a diagram)
Question 1:
1 | (a) | 41k0
k3 | M1
A1
[2] | 1.1a
1.1 | Consideration of i-component (allow
sign errors)
Sight of 3 scores both marks | k3 with no working
scores no marks
1 | (b) | e.g. taking moments about O: 4(k) – 3(2)
6
clockwise | M1
A1
B1
[3] | 1.1a
1.1
2.5 | Taking moments correctly about any
point with correct number of terms
oe (could be seen on a diagram)
Three forces represented by the vectors $-4\mathbf{i} + \mathbf{j} + 2\mathbf{j}$ and $k\mathbf{i} - 2\mathbf{j}$ act at the points with coordinates $(0, 0)$, $(3, 0)$ and $(0, 4)$ respectively.

\begin{enumerate}[label=(\alph*)]
\item Given that the three forces form a couple, find the value of $k$. [2]
\item Find the magnitude and direction of the couple. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2019 Q1 [5]}}
This paper (13 questions)
View full paper
Q1 5 Q2 4 Q3 5 Q4 6 Q5 7 Q6 7 Q7 8 Q8 11 Q9 12 Q10 8 Q11 14 Q12 16 Q13 17