Calculating Tensions in a Two-Rope System Supporting a Steel Beam

[Cursed]

Homework Statement

A 1000 kg steel beam is supported by two ropes. What is the tension in each?

Homework Equations

F = ma = mg

The Attempt at a Solution

I labeled the left tension as T_{1} and the right tension as T_{2}.

\sum{F_{y}} = T_{1,y} + T_{2,y} -mg = 0

T_{1,y} = T_{1} cos(20^{o})

T_{2,y} = T_{2} cos(30^{o})

T_{1,y} = T_{2,y}​

\sum{F_{y}} = T_{2,y} + T_{2,y} -mg = 0

\sum{F_{y}} = 2T_{2,y} -mg = 0

2T_{2,y} = mg

2T_{2,y} = (1000kg)(9.8 m/s^2)

2T_{2,y} = 9800 N

T_{2,y} = 4900 N

T_{2} cos(30^{o}) = 4900 N

T_{2} = 5658 N

For T_{1}, I get 5214 N.

That answer is wrong. The answer should be 6397 N and 4376 N.

 

[tiny-tim]

Hi Cursed!

T_{1,y} = T_{2,y}

Why??

And what about the x-components?

 

[Cursed]

Yeah. I figured that's probably where I went wrong.

I don't know how else to relate the two tensions. :S

 

[tiny-tim]

Yeah. I figured that's probably where I went wrong.

I don't know how else to relate the two tensions. :S

Hint: use the x-components!