Will Either Rope Break Supporting a 1000kg Steel Beam?

[circuscircus]

Homework Statement

A 1000kb steel beam is supported by two ropes. Each rope as a maximum sustained tension of 6000N. Does either rope break? If so, which one(s)?

http://img101.imageshack.us/img101/3930/diagramgm2.jpg

Homework Equations

Tension = M cos/sin theta
(in this case it is cos)

The Attempt at a Solution

Rope1 = 6000cos20 = 5638N
Rope2 = 6000cos30 = 5196N
W=1000*9.8 = 9800N / 2 = 4900N so no It does not break, but the answer says rope 1 breaks first and then rope 2

 

[bob1182006]

the equations you used are wrong. as well as the angles you used.

you need to use F=ma for the x and y components and you will get 2 equations of 2 variables which you can solve as a matrix or plugging it into your calculator.

for the x-component the tensions cancel out right?
and for the y-component the tensions will equal to the weight of the beam?

 

[m2003]

.

I would first clarify the parameters and assumptions of the problem. Are the ropes assumed to be ideal and have no defects? Are they attached to the beam and supports perfectly? Are there any external forces acting on the beam or ropes? Once these are established, I would then proceed to analyze the problem using the given data and relevant equations.

Based on the given information, it is possible for either rope to break, depending on the assumptions and calculations used. However, based on the calculations provided in the attempt at a solution, it appears that neither rope will break under the given conditions.

Using the equation for tension, it can be seen that the tension in both ropes is well below their maximum sustained tension of 6000N. Additionally, the weight of the beam is evenly distributed between the two ropes, so each rope is only supporting 4900N, which is well below their maximum sustained tension. Therefore, it is unlikely that either rope would break under these conditions.

However, it is important to note that in real-world situations, there may be additional factors that could affect the stability of the ropes, such as wind or vibrations. It is also possible that the ropes may have defects or wear and tear that could weaken them over time. These factors should be taken into consideration when determining the likelihood of either rope breaking.

Overall, based on the given information and calculations, it is unlikely that either rope will break under the given conditions. However, it is important to consider all factors and assumptions when analyzing a problem like this.