Maximum separation of points A and B before rope breaks at 4000N tension

[atagl1]

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!

 

[SteamKing]

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.

 

[voko]

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"?

 

[atagl1]

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.

 

[voko]

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.