Find Maximum Separation of Points A & B with 4000N Tension in Ropes

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In summary, the task is to determine the maximum separation between points A and B in order to safely raise a speaker without breaking the ropes. The ropes form an isosceles triangle with the ceiling and each have a magnitude of 370.6 N. The maximum tension allowed in the ropes is 4000 N, and the speaker weighs 50kg.
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The speaker is to be raised by increasing the separation between the points A
and B, but the ropes will break if the tension exceeds 4000 N. Find the maximum
possible separation between A and B; that is, when
the tensions in the ropes are equal to 4000 N.

The points are originally 6m apart, they make an angle of 41.4° with the ceiling, the magnitude of each rope is 370.6 N and the speaker weighs 50kg.


I'm completely unsure of how to start!
 
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  • #2
I would start by drawing a sketch of the speaker and the two ropes as described in the OP. Then, using a free-body diagram, I would determine the distance between A and B such that the speaker is supported and the total tension in the rope < 4000 N.
 
  • #3
Do the ropes and the ceiling form an isosceles triangle? And what does this really mean: "the magnitude of each rope is 370.6 N"?
 
  • #4
Yeah the ropes and the ceiling form an isosceles triangle. I'm not sure about the magnitude, that was just apart of the information given.
 
  • #5
Is this exactly how the problem was worded? "The magnitude of a rope" does not make any sense to, plus it seems to be in the units of force. Could that be the initial tension in them?

Anyway, stick with SteamKing's advice for now.
 

1. What is the purpose of finding the maximum separation of points A & B with 4000N tension in ropes?

The purpose of finding the maximum separation of points A & B with 4000N tension in ropes is to determine the maximum distance that can be achieved between two points when a specific amount of tension is applied to two ropes connected to those points. This information is useful in various engineering and construction applications, such as determining the maximum span of a bridge or the maximum length of a suspension cable.

2. How is the maximum separation of points A & B calculated?

The maximum separation of points A & B is calculated by using the formula: maximum separation = tension in ropes / weight per unit length of ropes. In this case, the tension is 4000N and the weight per unit length of the ropes is a known value that depends on the type and size of the ropes being used.

3. What factors can affect the maximum separation of points A & B?

The maximum separation of points A & B can be affected by several factors, such as the strength and weight of the ropes, the angle at which the ropes are attached to the points, and the stability and weight-bearing capacity of the points themselves. Other external factors, such as wind or other forces acting on the ropes, can also impact the maximum separation.

4. How is the tension in the ropes determined?

The tension in the ropes can be determined by using a tension meter or by conducting tension tests on the ropes. These tests involve applying a known amount of force to the ropes and measuring the resulting tension. The maximum tension that the ropes can withstand without breaking is then used in the calculation for the maximum separation of points A & B.

5. What safety precautions should be taken when conducting experiments to find the maximum separation of points A & B?

When conducting experiments to find the maximum separation of points A & B, it is important to follow all safety protocols and precautions. The ropes and attachment points should be inspected for any signs of wear or damage before conducting the experiment. It is also important to use proper safety equipment, such as gloves and safety glasses, and to have a trained professional supervise the experiment. Additionally, it is important to conduct the experiment in a controlled environment to minimize any potential risks.

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