Tension and Equilibrium

  • Thread starter wmrunner24
  • Start date
  • #1
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Homework Statement


Hint: sin^2 [tex]\Theta[/tex] + cos^2[tex]\Theta[/tex] = 1 .
Consider the 600 N weight held by two
cables shown below. The left-hand cable had
tension 440 N and makes an angle of [tex]\Theta[/tex]2 with
the ceiling. The right-hand cable had tension
480 N and makes an angle of [tex]\Theta[/tex]1 with the
ceiling. What is the angle [tex]\Theta[/tex]1 which the right-
hand cable makes with respect to the ceiling?
Answer in units of ◦.

Physics3.jpg


Homework Equations


[tex]\Sigma[/tex]Fx=0
[tex]\Sigma[/tex]Fy=0


The Attempt at a Solution



So, I understand all of the concepts perfectly well in order to complete this problem. The net force in both the x and y direction must be 0 in order for the system to remain at rest. Thus:

T1sin[tex]\Theta[/tex]1+T2sin[tex]\Theta[/tex]2=mg
T1cos[tex]\Theta[/tex]1=T2cos[tex]\Theta[/tex]2

In these two equations there are two unknowns: the two [tex]\Theta[/tex]s. So, if I solve for one, I can find the other. However, the issue here is the algebra. I'm not sure how to solve when I have cosine nested in arcsine, and such. Usually, I would turn to my TI-89 Titanium to solve this but it freezes. So, how am I to proceed? Any help is appreciated.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
For this equation

T1cosθ1=T2cosθ2

Try squaring both sides and then use the hint to get a new equation in terms of sine.
 
  • #3
58
0
Genius. Worked great. Thanks a bunch.
 

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