Finding The Tension force with different angles

[Ashleyz]

Homework Statement

I have done all the physics for this problem which I'll detail below. I am only having trouble in doing the simple math to single out the t1 or t2.

A mass is hanging from a ceiling. It is supported by two strings which both are attached above to the ceiling. String 1 is at an angle of 30. String 2 is at an angle of 65. While the
mass is 20 lb. ( in the center)

Homework Equations

Ma = 0 in both the x and y directions.

The Attempt at a Solution

left T (T1) =30 degrees

right T (T2) = 65 degrees.

ok, here are my equations that I get to:

X: T2cos(65) - T1cos(30) = 0

Y: T2sin(65) + T1sin(30) = 0

now I just need to solve for, say, T1 in the x dierection and use that new eq. to
pluge into Y. Right?

 

[PhanthomJay]

The 20 pounds is the value of the weight of the hanging mass; it is not the mass. In your last equation in the y direction, you are missing a force.

 

[Ashleyz]

right. I am missing -w. Sorry about the mistake.

Now what of the T that I need to solve for. I have Solved for the T in my
x and y equation and get bad nasty answers.

 

[PhanthomJay]

First plug in the value for cos 65, sin 65, etc. Then solve the 2 equations with the 2 unknowns as you see fit.

 

[Ashleyz]

Do you mean this:

I'll take the x eq. and solve for t1.

I get T1 = T2cos(65) / cos (30)

now I can take this eq. for T1 and plug it in for T1 in the y eq?

 

[PhanthomJay]

It will be a lot easier if you rewrite your first equation as T1= T2(.423)/.866 = 0.49T2. Rewrite the 2nd equation in the same manner, then do the substitution.

 

[Ashleyz]

It will be a lot easier if you rewrite your first equation as T1= T2(.423)/.866 = 0.49T2. Rewrite the 2nd equation in the same manner, then do the substitution.

I see.

T1 = T2(.49)

T2 = 21.74lb + T1(.54) I divided .92 into lbs., think you can do that.

now ill put T2 in the T1 eq. Right?