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

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SUMMARY

The discussion focuses on solving a statics problem involving a pulley and cables, specifically using the equations of equilibrium for forces in the x and y directions. The participant, @MecEngPterois, initially calculated a tension of 2391N but received incorrect feedback. The correct equations derived from the free body diagram are Tcos(25) - (T + P)cos(55) = 0 and Tsin(25) + (T + P)sin(55) - Q = 0, where Q is given as 1860N. The community encourages detailed work to identify the correct solution.

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MecEngPterois
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Thread moved from the technical forums to the schoolwork forums
What I did was split the problem into two separate 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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