Standard +0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions to form two simultaneous equations. While it involves trigonometry and solving for two unknowns, it's a routine textbook exercise with a clear method that A-level mechanics students practice extensively. Slightly easier than average due to its straightforward approach.
\includegraphics{figure_1}
Coplanar forces of magnitudes 40 N, 32 N, \(P\) N and 17 N act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of \(P\) and \(\theta\). [6]
Question 1:
1 | [P cos θ = 32 cos 20 – 17 sin 55]
[P sin θ = 40 + 17 cos 55 – 32 sin 20] | M1 | Resolve forces horizontally or vertically
3 terms horizontally, 4 terms vertically
A1 | One correct
A1 | Both correct
[P sin θ = 38.8062 P cos θ = 16.1446]
P= ( 17cos55−32sin20+40 )2 +( 32cos20−17cos35 )2 | M1 | Either use Pythagoras to find P
or use their value of θ to find P
(17cos55−32sin20+40)
θ =tan−1
(32cos20−17cos35) | M1 | Either use trigonometry to find θ
or use their value of P to find θ
[tan θ = 2.4037]
P = 42(.0) and θ = 67.4 | A1
6
Question | Answer | Marks | Guidance
\includegraphics{figure_1}
Coplanar forces of magnitudes 40 N, 32 N, $P$ N and 17 N act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of $P$ and $\theta$. [6]
\hfill \mbox{\textit{CAIE M1 2019 Q1 [6]}}