Moderate -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.
\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:
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]}}