Supporting 1100kg Steel Beam w/ 6200N Ropes

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In summary, a 1100 kg steel beam is supported by two ropes with a maximum sustained tension of 6200 N. Using the equations Fnet = ma and the sum of forces in the x and y directions, it was determined that the tension in the ropes R1 and R2 are 6645.96 N and 4546.11 N respectively. However, after realizing that the cosine term was dropped, the correct values are 6645.96 N and 5454.55 N for R1 and R2.
  • #1
spin360
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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?
 
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  • #2
spin360 said:
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).
 
  • #3
Doc Al said:
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?
 
  • #4
The cosine you dropped is the one right here:
spin360 said:
R1*cos(20) + R2*cos(30) - Mg = 0
R1*cos(20) + R2*cos(30) = Mg = 10791 N
 
  • #5
oh wow what a stupid mistake, thanks! it works now
 

1. What is the maximum weight that can be supported by the 6200N ropes?

The 6200N ropes can support a maximum weight of 1100kg, which is equivalent to approximately 2425 pounds.

2. How is the weight of the steel beam distributed between the 6200N ropes?

The weight of the steel beam is evenly distributed between the 6200N ropes, with each rope supporting approximately 275kg.

3. Can the 6200N ropes be replaced with ropes of a different strength?

Yes, the 6200N ropes can be replaced with ropes of a different strength as long as they can support the weight of the steel beam and are properly secured.

4. What factors should be considered when selecting ropes to support the 1100kg steel beam?

The factors to consider when selecting ropes to support the 1100kg steel beam include the strength and weight capacity of the ropes, the durability and material of the ropes, and the proper anchoring and securing of the ropes.

5. How many ropes are necessary to safely support the 1100kg steel beam?

The number of ropes needed to safely support the 1100kg steel beam may vary depending on the strength and weight capacity of the ropes, but at least four 6200N ropes are recommended for optimal support and stability.

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