Why Does This Statics Solution Use These Specific Equations?

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Discussion Overview

The discussion revolves around the specific equations used in a statics problem involving forces and tensions in a pulley system. Participants explore the reasoning behind the application of trigonometric functions and the relationships between different tensions in the system. The scope includes technical explanations and conceptual clarifications related to statics and equilibrium in physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant calculated an angle using arctan and questioned the addition of 180 degrees, suggesting that the angle could be determined simply as tan^-1(12/5).
  • Another participant emphasized the importance of drawing a free body diagram (FBD) to find force vector components, indicating that the numerical value of the angle may not be necessary.
  • Concerns were raised about the assumption that tensions in cords CD and BC are both 100 lbs, with a participant noting that tensions around frictionless pulleys should be equal on both sides.
  • There was confusion regarding the formation of the equations used in the solution, with requests for clarification on how the equations were derived based on the equilibrium of the system.
  • Participants discussed the relationship between tensions in different cords, specifically whether tensions in AC and BC are equal, and clarified that the tension in BC does not equal the tension in DC.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding tension values and the necessity of specific angles in the calculations. There is no consensus on the correct approach to deriving the equations or the assumptions made in the problem.

Contextual Notes

Participants highlight potential limitations in their assumptions about tension values and the need for accurate free body diagrams to clarify the relationships between forces in the system. The discussion remains focused on the derivation of equations and the interpretation of forces without resolving the underlying assumptions.

akhmed966
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http://img10.imageshack.us/img10/8880/capturejfu.jpg

I did arctan(12/5) to get the degrees + 180 to get the angle from the X axis to B, then I just split the angles into components.

I did 100*cos(246) + 100*cos(theta) = 0, and I got 67 degrees.
Then I was doing the Y components, and realized they were equal and opposite, so it would equal 0, which the weight can't be equal to.

So I looked at the solution, and here how the answer is found.

Sum of X: 100cos(theta) = Wa(5/13)
Sum of Y: 100sin(theta) = Wa(12/13)+Wa

Why is the answer figured like this, and when do I do it differently from sum of the components? I'm totally lost, but I have a slight idea.

Thanks.
 
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Why, did you add the 180 degrees? Assuming the x-axis is at the center of the pully the angle is simply tan^-1(12/5)?

Also, draw a simple free body diagram to find the force vector components. You will find the actual numerical value of the angle is not needed.

Thanks
Matt
 
Last edited:
I meant the positive X axis.

Also, I did draw a free body diagram, but I am not sure why I couldn't add the sum of the components.
 
You seem to be assuming that the tension in cord CD and BC are both 100 lbs. That is not correct. Also, you are not noting that the tension in cords draped around frictionless ideal pulleys are the same on both sides of the wrap (that is, Tension in AC = Tension in BC). Draw an FBD of the hanging weight, and redo your FBD of the pulley at joint C.
 
The tension in AC = BC? Do you mean the tension in BC = DC?

I still don't see how the equation was formed, could someone explain how the equation was determined?
 
akhmed966 said:
The tension in AC = BC?
Yes. The cord ACB is one continuous chord wrapped around an ideal pulley, in which case AC = BC.
Do you mean the tension in BC = DC?
No.
I still don't see how the equation was formed, could someone explain how the equation was determined?
The system is in equilibrium. Draw a FBD of the weight to determine that the tension in AC must be W_a. Then draw an FBD of the pulley at C, and you should be able to get the same equations as the book's to solve for theta and W_a. Which cord do you think has the 100 pound tension load?.
 

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