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!