Confused about resolving Tension and Weight

[laser]

Homework Statement

Confused about resolving Tension and Weight

Relevant Equations

uhh

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!

 

[TSny]

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.

Relevant Equations: uhh

Can you list any relevant equations for the forces when you have static equilibrium?

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

These look right.

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.

 

[laser]

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.

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)

 

[TSny]

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.

 

[berkeman]

Oops, probably posted in the wrong forum. This isn't a homework, question, just something I was wondering about.

Any question that is schoolwork-like belongs in the schoolwork forums and we require that you show lots of work.

https://www.physicsforums.com/threads/homework-coursework-questions.373889/