Help needed with a Statics Question: Load is supported by a Pulley and Cables

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The discussion revolves around solving a statics problem involving a pulley and cables, where the user has set up equations based on x and y coordinates to find tension (T) in the system. The user initially calculated the tension to be 2391N but received incorrect feedback. Another participant suggests refining the equations by considering the balance of forces on the pulley, offering a more detailed approach to the problem. They emphasize the importance of understanding the mechanics behind the forces involved, likening it to the ease of pulling a bowstring versus bending the bow itself. The conversation aims to help the user find the correct solution to the statics question.
MecEngPterois
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What I did was split the problem into two seperate summations based on x & y coordinates:

Tcos(25) - Tcos(55) - Px = 0
Tsin(25+Tsin(55) +Py - Q = 0,

Where Q = 1860

I initially got an answer of 2391N, but it keeps marking me wrong for said answer.

This is the free body diagram, (the previous question asked me to construct) that I am basing my work off of:

Screenshot 2023-09-07 132413.png
Here is the question.
Screenshot 2023-09-07 132108.png
 
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Welcome, @MecEngPterois !

Could you show us your work in detail?

Think of the principle behind a bow and an arrow.
Is it easier for the hand to initiate the pulling of the cord than directly bending the bow?
 
The horizontal and vertical force balances on the pulley F should read:
$$T\cos{25}-(T+P)\cos{55}=0$$. $$T\sin{25}+(T+P)\sin{55}-Q=0$$
 
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