Standard +0.3 This is a standard two-dimensional equilibrium problem requiring resolution of forces in two perpendicular directions to find two unknowns. While it involves trigonometry and simultaneous equations, it's a routine mechanics exercise with a clear method that students practice extensively. The 4-mark allocation confirms it's straightforward application rather than problem-solving.
\includegraphics{figure_3}
Coplanar forces of magnitudes \(52\) N, \(39\) N and \(P\) N act at a point in the directions shown in the diagram. The system is in equilibrium.
Find the values of \(P\) and \(\theta\). [4]
Allow sin/cos mix. only – or for P2 =392 +522or tan= .
39
(allow reciprocal for M mark).
Answer
Marks
Guidance
Pcos=39 Psin=52
A1
52
Both correct – or for both P2 =392 +522 and tan= .
39
P= 392 +522
52
=tan−1
Answer
Marks
Guidance
39
DM1
Attempt to solve for either P or θ from equations with the correct
number of relevant terms.
OE using sin/cos with P
Answer
Marks
Guidance
P = 65 =53.1
A1
Both correct; 53.13010…
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 3:
3 | Resolving in any direction to get an equation | *M1 | 52
Allow sin/cos mix. only – or for P2 =392 +522or tan= .
39
(allow reciprocal for M mark).
Pcos=39 Psin=52 | A1 | 52
Both correct – or for both P2 =392 +522 and tan= .
39
P= 392 +522
52
=tan−1
39 | DM1 | Attempt to solve for either P or θ from equations with the correct
number of relevant terms.
OE using sin/cos with P
P = 65 =53.1 | A1 | Both correct; 53.13010…
4
Question | Answer | Marks | Guidance
\includegraphics{figure_3}
Coplanar forces of magnitudes $52$ N, $39$ N and $P$ N act at a point in the directions shown in the diagram. The system is in equilibrium.
Find the values of $P$ and $\theta$. [4]
\hfill \mbox{\textit{CAIE M1 2024 Q3 [4]}}