CAIE M1 2014 June — Question 3 6 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2014
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeEquilibrium of particle under coplanar forces
DifficultyModerate -0.5 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions and solving simultaneous equations. While it involves multiple forces at angles, the method is routine and well-practiced in M1 courses, making it slightly easier than average but still requiring careful calculation.
Spec3.03b Newton's first law: equilibrium3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0

\includegraphics{figure_3} A particle is moving under the action of three forces as shown in the diagram. The particle is in equilibrium. Find the magnitudes of forces \(P\) and \(Q\). [6]

Question 3:
AnswerMarks
3o o
X = 5 – 7cos 60 – 3cos 30 (= – 1.098)
o o
Y = 7sin 60 – 3sin 30 – 4 (= 0.5622)
Resultant is 1.23 N and
o
Direction is 152.9 anticlockwise from
AnswerMarks
+ve x-axis oeM1
A1
M1
A1
M1
AnswerMarks Guidance
A1[6] For finding the component of the forces in
the x direction
For finding the component of the forces in
the y direction
2 2 2
For using R = X + Y and tan θ = Y/X
Question 3:
3 | o o
X = 5 – 7cos 60 – 3cos 30 (= – 1.098)
o o
Y = 7sin 60 – 3sin 30 – 4 (= 0.5622)
Resultant is 1.23 N and
o
Direction is 152.9 anticlockwise from
+ve x-axis oe | M1
A1
M1
A1
M1
A1 | [6] | For finding the component of the forces in
the x direction
For finding the component of the forces in
the y direction
2 2 2
For using R = X + Y and tan θ = Y/X
\includegraphics{figure_3}

A particle is moving under the action of three forces as shown in the diagram. The particle is in equilibrium.

Find the magnitudes of forces $P$ and $Q$. [6]

\hfill \mbox{\textit{CAIE M1 2014 Q3 [6]}}