OCR M1 2010 June — Question 3 9 marks

Exam BoardOCR
ModuleM1 (Mechanics 1)
Year2010
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeBearing and compass direction problems
DifficultyModerate -0.3 This is a straightforward vector resolution problem requiring students to resolve forces into components along given directions and find the resultant. While it involves multiple steps and bearing conversions, the techniques are standard M1 material with no novel problem-solving required. The 'show that' in part (i) provides confirmation of correct working, making it slightly easier than average.
Spec3.03p Resultant forces: using vectors

3 \includegraphics[max width=\textwidth, alt={}, center]{4b703cf9-b3d3-4210-b57b-89136595f8a5-02_570_495_1114_826} Three horizontal forces of magnitudes \(12 \mathrm {~N} , 5 \mathrm {~N}\), and 9 N act along bearings \(000 ^ { \circ } , 150 ^ { \circ }\) and \(270 ^ { \circ }\) respectively (see diagram).
  1. Show that the component of the resultant of the three forces along bearing \(270 ^ { \circ }\) has magnitude 6.5 N .
  2. Find the component of the resultant of the three forces along bearing \(000 ^ { \circ }\).
  3. Hence find the magnitude and bearing of the resultant of the three forces.

3\\
\includegraphics[max width=\textwidth, alt={}, center]{4b703cf9-b3d3-4210-b57b-89136595f8a5-02_570_495_1114_826}

Three horizontal forces of magnitudes $12 \mathrm {~N} , 5 \mathrm {~N}$, and 9 N act along bearings $000 ^ { \circ } , 150 ^ { \circ }$ and $270 ^ { \circ }$ respectively (see diagram).\\
(i) Show that the component of the resultant of the three forces along bearing $270 ^ { \circ }$ has magnitude 6.5 N .\\
(ii) Find the component of the resultant of the three forces along bearing $000 ^ { \circ }$.\\
(iii) Hence find the magnitude and bearing of the resultant of the three forces.

\hfill \mbox{\textit{OCR M1 2010 Q3 [9]}}