Finding an angle with Newton's Second Law

AI Thread Summary
To find the angle θ in a free-body diagram where the body is in equilibrium, Newton's second law is applied in the y-direction. The initial calculations were incorrect due to misunderstanding the vector relationships of the forces, which have equal magnitudes but different directions. The correct approach involves using cos(θ/2) or sin(90° - θ/2) to relate the forces. Ultimately, the angle θ is determined to be 120 degrees. This highlights the importance of accurately considering vector components in equilibrium problems.
Mr Davis 97
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Homework Statement


Given the free-body diagram below, and that the body is in equilibrium, find θ.
ee3VjBf.jpg

Homework Equations


F = ma

The Attempt at a Solution


[/B]
Basically, I used Newton's second law in the y direction.

Here is my work:
o4KjcyS.jpg

This does not seem like the correct answer, because the angle is acute. Thus, what am I doing wrong?
 
Last edited:
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Mr Davis 97 said:

Homework Statement


Given the free-body diagram below, and that the body is in equilibrium, find θ.
[ IMG]http://i.imgur.com/ee3VjBf.jpg[/PLAIN]

Homework Equations


F = ma

The Attempt at a Solution


[/B]
Basically, I used Newton's second law in the y direction.

Here is my work?
[ IMG]http://i.imgur.com/o4KjcyS.jpg[/PLAIN]
This does not seem like the correct answer, because the angle is acute. Thus, what am I doing wrong?
First of all, the three forces may have equal magnitude, but they are not equal as vectors.

That should be cos(θ/2) or equivalently sin(90° - θ/2)
 
SammyS said:
First of all, the three forces may have equal magnitude, but they are not equal as vectors.

That should be cos(θ/2) or equivalently sin(90° - θ/2)
So θ = 120 degrees?
 
Last edited:
Mr Davis 97 said:
So θ = 120 degrees?
Yes.
 
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