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

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Discussion Overview

The discussion revolves around a statics problem involving a load supported by a pulley and cables. Participants are analyzing the forces acting on the system, using free body diagrams and equilibrium equations to solve for tensions and loads. The focus is on the mathematical reasoning and application of static equilibrium principles.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents a system of equations based on the x and y components of forces, leading to an initial tension calculation of 2391N, which is marked incorrect.
  • Another participant suggests showing detailed work and draws an analogy to the mechanics of a bow and arrow to illustrate the principles involved.
  • A third participant proposes an alternative set of equations for the horizontal and vertical force balances on the pulley, indicating a different approach to the problem.
  • There is a request for the original poster to find the correct solution, indicating an ongoing search for resolution.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the correct approach or solution to the problem. Multiple competing views and methods are presented without agreement on which is correct.

Contextual Notes

There are unresolved mathematical steps and assumptions in the equations presented, and the dependence on the accuracy of the free body diagram is noted but not clarified.

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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