Tension on ropes

spin360

1. The problem statement, all variables and given/known data
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.


2. Relevant equations
Fnet = ma


3. 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

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

spin360

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

spin360

here is the problem

Doc Al

The cosine you dropped is the one right here:

spin360

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