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

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To find the maximum separation between points A and B while maintaining a tension of 4000 N in the ropes, a free-body diagram is essential. The initial distance between A and B is 6m, with the ropes forming an isosceles triangle at a 41.4° angle with the ceiling. Each rope's tension is noted as 370.6 N, which may refer to the initial tension rather than the maximum allowable tension. The goal is to ensure that the total tension does not exceed 4000 N while supporting the speaker's weight of 50 kg. Understanding these parameters is crucial for solving the problem effectively.
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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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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.
 
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"?
 
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.
 
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.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
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