Laws of Motion with Static Equilibrium

AI Thread Summary
The discussion focuses on solving a static equilibrium problem involving two weights and tensions in ropes. The user attempts to find the angles and tensions using equations related to forces and trigonometry but struggles to obtain the correct answers. They clarify that the vertical component of tension T_1 corresponds to the weight w_1, leading to a calculation of T_1 as 17.447 N. The conversation also touches on the role of pulleys in changing the direction of tension without affecting its magnitude. The user seeks confirmation on their approach and calculations regarding the tensions in the ropes.
Keithkent09
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Homework Statement


Find θ and W in the figure below where w1 = 16.0 N, w2 = 25.0 N, and α = 66.5°, assuming that the arrangement is at rest.

Homework Equations


T_1=25/sin(alpha)
F_x=-T_1cos(alpha)+T_2cos(theta)
F_y=T_1sin(alpha)+T_2sin(theta)-2

The Attempt at a Solution


I tried to use the above equations to solve for the three unknowns. First I found the tension of the string on the left, then plugged that into the second two equations to find the remaining values and I could not get the correct answers.
 

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Keithkent09 said:
T_1=25/sin(alpha)

Why is this true? What are tensions T1 and T2 in each rope?
 
Sorry I meant that it is 16/sin(alpha).
This is because the vertical component of T_1 is 16 because of w_1. So using trig T_1=17.447. I am doing this the correct way and just making some kind of simple mistake?
 
A pulley changes the direction of the tension without changing its magnitude. What is the tension in the piece of the leftmost rope that is hanging straight down?
 
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