How can I solve for W in this tricky statics problem without exceeding 1050N?

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Discussion Overview

The discussion revolves around solving a statics problem involving a hanging weight (W) and two tension forces (T1 and T2) that must not exceed 1050N. Participants explore the relationships between these forces using equations derived from a free body diagram and discuss various approaches to find the value of W while adhering to the constraints provided.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant describes their struggle with the problem, noting the given tension T3 as 680N and the slope as 8/5, which complicates their analysis.
  • Another participant provides two equations that relate T1, T2, and W, suggesting substituting 1050N for either T1 or T2 to solve for the other tension and subsequently for W.
  • A later reply indicates that substituting 1050N for T2 leads to a calculated W of 609N, while T1 is found to be 544N, acknowledging initial confusion caused by T3.
  • Another participant emphasizes the presence of three unknowns (T1, T2, W) and two equations, suggesting a method to maximize one of the inequalities to simplify the problem-solving process.

Areas of Agreement / Disagreement

Participants generally agree on the approach of substituting values into the equations to find W, but there is no consensus on the best method to handle the inequalities or the implications of T3 on the overall solution.

Contextual Notes

Participants note the presence of multiple unknowns and equations, as well as the need to manage inequalities, which may complicate the solution process. The discussion reflects varying levels of understanding and approaches to the problem.

Who May Find This Useful

Students and individuals interested in statics problems, particularly those involving tension forces and weight calculations, may find this discussion beneficial.

paul11273
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I am having trouble with a HW question that has been driving me crazy for a few days now. I have to solve for W ( a hanging weight) that will not cause either T1 or T2 to exceed 1050N. So far I have drawn the free body diagram that is attached as a word doc, and the angles I found based on the dimensions given. The problem gives T3 as 680N and shows the slope to be 8/5. This causes (I think) T3 and T2 to be directly in line with each other. I feel like I am letting this fact throw me off. Also, when I start trying to break up each one into component vectors, it seems that I have too many unknowns. I have tried several different approaches but each leads me to an incorrect answer. The book gives a range for W of 0 < W < 609N.
Can you help me figure this one out? Atleast lead me in the right direction? Thanks.
 

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These are the two equations:

1. cos(28)T2 - cos(53)T1 = cos(28)680
2. sin(53)T1 + sin(28)T2 - sin(28)680 = W

You are trying to find W where T1 or T2 is equal to 1050. So substitute 1050 in for T1 or T2, and solve for the other T. Then solve for the weight.
 
Thanks!
I can't believe that I killed myself over this question. I had those two equations, but failed to see that I need to sub in 1050 for either T1 or T2, then solve for the other.
I have completed it, and found that T2 will be 1050N when the W is 609N, and T1 will 544N.
I let T3 confuse me, and it had me thinking the problem would be more complicated.
Thanks again. You have sold me on this forum. I will check here regularly, and hopefully I can contribute as well.
 
You have 3 unknowns: T1, T2, and W
You have 2 equations, as Moose pointed out.
You also have 2 inequalities, one of which you must "max out", and the other of which you must ensure holds. Pick one of the inequalities, arbitrarily, and max it out (turn it into an equality). This fixes one of your unknowns (T1 or T2, whichever you chose). Then, solve the equations, and afterwards make sure the other inequality holds. If it does not, then just go back and max out the other inequality and solve.
 

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