How Should Angles Be Used in Calculating Tension Forces?

[cbchapm2]

Homework Statement

See attached figure below for problem:

I'm designating the "horizontal cable" T1, the "incline cable" T2, and the "vertical cable" T3.

Homework Equations

I used the following to find x and y components of each force:
x comp=Tncos(theta)
y comp=Tnsin(theta)

The Attempt at a Solution

I made a chart for T1, T2, and T3 for the respective x and y components.
T1:
x=T1cos(180)
y=0 (because it's only the x direction)
I didn't know which angle to use for theta, I used 180 because of where I put the x and y-axis in my free body diagram.

T2:
x=T2cos(38)
y=T2sin(38)
Again, I didn't know if I should use the 38* or add 180 to it...

T3:
x=0 (because it's only in the y direction?)
y=532 N (given)

I started to sum my x components and then solve for T2, but the answer that I got was wrong. I did this:
Sun of x components: 0=T1cos(180)+T2cos(38)
T2=T1(cos(180)/cos(38))
T2=1.27 N
I tried both 38* and 218* for the theta of T2 and both answers were wrong.

Sum of y components: 0=T1sin(180)+T2sin(38)+532N
Once I got the correct value for T2, I would plug it into this equation to find T1. And T3 will equal the weight (532 N) because of equilibrium, right?

Can anyone help me get on the right track?

Thanks!

 

[haruspex]

Sun of x components: 0=T1cos(180)+T2cos(38)
T2=T1(cos(180)/cos(38))

You've switched the sign there.

T2=1.27 N

Where did that come from?

Sum of y components: 0=T1sin(180)+T2sin(38)+532N

To be consistent with the signs, that should be -532N (sin(270)=-1).

 

[SteamKing]

You have some confusion with angles. The convention is that the positive x- axis has angle 0 degrees, and the angle increases as one goes counterclockwise. Therefore, positive y is 90 degrees, negative x is 180 degrees and negative y is 270 degrees.

 

[cbchapm2]

I got the right answer! When I solved the first equation for T2, I dropped the T1 and it threw off everything else too.

 

[Nickie]

I would suggest reviewing the concept of tension force and the correct equations for finding the x and y components. The angle theta should be the angle between the cable and the horizontal axis, not the angle of the cable itself. Additionally, the equation for summing the x components should be T1cos(theta)-T2cos(38), and the equation for summing the y components should be T1sin(theta)+T2sin(38)-532N. This will give you the correct values for T1 and T2. Also, remember to use the correct units for your calculations. Good luck!