OCR MEI M1 2006 January — Question 3 7 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2006
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeParallel or perpendicular vectors condition
DifficultyModerate -0.8 This is a straightforward mechanics question testing basic vector operations: magnitude calculation using Pythagoras, bearing from arctan, recognizing parallel vectors as scalar multiples, and finding a component so the resultant is parallel to a given vector. All parts use standard techniques with no problem-solving insight required, making it easier than average.
Spec3.03a Force: vector nature and diagrams
3 A force \(\mathbf { F }\) is given by \(\mathbf { F } = ( 3.5 \mathbf { i } + 12 \mathbf { j } ) \mathrm { N }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors east and north respectively.
  1. Calculate the magnitude of \(\mathbf { F }\) and also its direction as a bearing.
  2. \(\mathbf { G }\) is the force \(( 7 \mathbf { i } + 24 \mathbf { j } )\) N. Show that \(\mathbf { G }\) and \(\mathbf { F }\) are in the same direction and compare their magnitudes.
  3. Force \(\mathbf { F } _ { 1 }\) is \(( 9 \mathbf { i } - 18 \mathbf { j } ) \mathrm { N }\) and force \(\mathbf { F } _ { 2 }\) is \(( 12 \mathbf { i } + q \mathbf { j } ) \mathrm { N }\). Find \(q\) so that the sum \(\mathbf { F } _ { 1 } + \mathbf { F } _ { 2 }\) is in the direction of \(\mathbf { F }\).
3 A force $\mathbf { F }$ is given by $\mathbf { F } = ( 3.5 \mathbf { i } + 12 \mathbf { j } ) \mathrm { N }$, where $\mathbf { i }$ and $\mathbf { j }$ are horizontal unit vectors east and north respectively.\\
(i) Calculate the magnitude of $\mathbf { F }$ and also its direction as a bearing.\\
(ii) $\mathbf { G }$ is the force $( 7 \mathbf { i } + 24 \mathbf { j } )$ N. Show that $\mathbf { G }$ and $\mathbf { F }$ are in the same direction and compare their magnitudes.\\
(iii) Force $\mathbf { F } _ { 1 }$ is $( 9 \mathbf { i } - 18 \mathbf { j } ) \mathrm { N }$ and force $\mathbf { F } _ { 2 }$ is $( 12 \mathbf { i } + q \mathbf { j } ) \mathrm { N }$. Find $q$ so that the sum $\mathbf { F } _ { 1 } + \mathbf { F } _ { 2 }$ is in the direction of $\mathbf { F }$.

\hfill \mbox{\textit{OCR MEI M1 2006 Q3 [7]}}
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