Confused about resolving Tension and Weight

AI Thread Summary
The discussion revolves around resolving tension and weight in a system at equilibrium, with the user confused about two sets of calculations. The first set of equations, T1sin(theta) + T2sin(theta) = W and T1cos(theta) = T2cos(theta), is deemed correct. However, the second set, Wsin(theta) = T1 and Wcos(theta) = T2, is identified as incorrect due to neglecting the relationship between T1 and T2, which are not perpendicular for general angles. Even at 45 degrees, the equations yield inconsistent results for weight, indicating a fundamental misunderstanding in the application of equilibrium principles. Clarification on the correct approach to resolving forces in static equilibrium is needed.
laser
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Homework Statement
Confused about resolving Tension and Weight
Relevant Equations
uhh
1700939433965.png


Calculations with 1:
T1sintheta + T2sintheta = W
T1costheta = T2costheta

Calculations with 2:
Wsintheta = T1
Wcostheta = T2

These are not equivalent. Can someone point out the flaw in my logic?

Edit: System is in equilibrium!
 
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laser said:
Homework Statement: Confused about resolving Tension and Weight
Welcome to PF!
When giving the Homework Statement, please give the full statement exactly as given to you.

laser said:
Relevant Equations: uhh
Can you list any relevant equations for the forces when you have static equilibrium?

laser said:
Calculations with 1:
T1sintheta + T2sintheta = W
T1costheta = T2costheta
These look right.

laser said:
Calculations with 2:
Wsintheta = T1
Wcostheta = T2

These are not equivalent. Can someone point out the flaw in my logic?

It's hard to follow your logic based on the little that you have written down. The equation ##W \sin \theta = T_1## is incorrect. I'm guessing that you neglected the fact that ##T_2## has a component parallel to ##T_1##. That is, ##T_2## is not perpendicular to ##T_1## for general values of ##\theta##. Likewise, your equation ##W \cos \theta = T_2## is incorrect.
 
TSny said:
When giving the Homework Statement, please give the full statement exactly as given to you.
Oops, probably posted in the wrong forum. This isn't a homework, question, just something I was wondering about.
TSny said:
It's hard to follow your logic based on the little that you have written down. The equation Wsin⁡θ=T1 is incorrect. I'm guessing that you neglected the fact that T2 has a component parallel to T1. That is, T2 is not perpendicular to T1 for general values of θ. Likewise, your equation Wcos⁡θ=T2 is incorrect.
Fair point, I agree with you.

Let's say theta = 45 degrees. That makes them perpendicular, but the equations still don't work out.

From calculation 1:
We get W = Tsqrt(2)

From calculation 2:
We get W=T/sqrt(2)
 
laser said:
Let's say theta = 45 degrees. That makes them perpendicular, but the equations still don't work out.

From calculation 1:
We get W = Tsqrt(2)

From calculation 2:
We get W=T/sqrt(2)
Check your equation for calculation 2.
 
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