Supporting 1100kg Steel Beam w/ 6200N Ropes

[spin360]

Homework Statement

A 1100 kg steel beam is supported by two ropes. Each rope has a maximum sustained tension of 6200 N.

Then it shows a diagram of two ropes holding a steal beam at the center, both are angled out. The rope on the left is angled away at 20 deg from y axis. The rope on the right is angled 30 deg from y axis.

Homework Equations

Fnet = ma

The Attempt at a Solution

So basically I used substitution...
R1 = rope 1 (left)
R2 = rope 2 (right)
E = summation
F = Force

E(Fx) = MAx = 0

R2*sin(30) - R1*sin(20) = 0
R2*sin(30) = R1*sin(20)
R2 = R1*[sin(20)/sin(30)]

Plug that into sum of forces in y direction...

E(Fy) = MAy = 0

R1*cos(20) + R2*cos(30) - Mg = 0
R1*cos(20) + R2*cos(30) = Mg = 10791 N
plug in R2...
R1*[cos(20) + sin(20)/sin(30)] = 10791
R1 = 6645.96 N

Now I did it like this.. plugged that back into the original and got 4546.11 N for R2. However it was wrong. So I thought okay since the max tension is supposedly 6200 I'll use that as R1 and got 4241.05 for R2. Wrong again. Any ideas?

 

[Doc Al]

R1*cos(20) + R2*cos(30) - Mg = 0
R1*cos(20) + R2*cos(30) = Mg = 10791 N
plug in R2...
R1*[cos(20) + sin(20)/sin(30)] = 10791
R1 = 6645.96 N

Redo your plugging in of R2; looks like you dropped the cos(30).

 

[spin360]

Redo your plugging in of R2; looks like you dropped the cos(30).

Not sure where you're getting the cos... both are sine since the x vector is opposite of the angle.. making it sine. Right?

 

[Doc Al]

The cosine you dropped is the one right here:

R1*cos(20) + R2*cos(30) - Mg = 0
R1*cos(20) + R2*cos(30) = Mg = 10791 N

 

[spin360]

oh wow what a stupid mistake, thanks! it works now