hhattiecc
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I seem to have a memory of doing a mechanics question which gave a bead on a string with both ends suspended to a horizontal ceiling so that the bead hung below. It gave the angles between each end of the string and the ceiling, and then asked you to find the weight of the bead knowing that the system was in equilibrium. I figured that the only way to do it was by working on the basis that the tension in each part of the string was equal, which got me the right answer, but now I'm wondering why?

My question is under what conditions is the tension in the strings the same? Is it when the 'strings' are actually just one string (so like with the bead for example, the string on either side is still the same piece of string)?

Ooop just had a thought: when a bead/particle is suspended by strings/string, the tensions must be the same as long as the angles made with the horizontal are the same (so their horizontal components cancel), so is that the defining condition for equal tension? In theory, could a bead on a rough string be suspended so that it doesn't lie in the centre of the string, meaning that the ends of the string make different angles with the horizontal and so have different tensions?

Also, why is the tension in each part of the light string in a particle-pulley system equal?

Hopefully this made some sense, and thanks in advance :-)
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AScarecrowsWit
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I thought that the tension was the same in the string because it is one string so the tension can't be different..? I'm unsure though
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Alexion
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(Original post by AScarecrowsWit)
I thought that the tension was the same in the string because it is one string so the tension can't be different..? I'm unsure though
If the angles are different, then the tensions in the two parts of the string have to be different.

Otherwise the horizontal components of the force wouldn't cancel out, and the bead would start accelerating to one side...
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lukejoshjames
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(Original post by hhattiecc)
In theory, could a bead on a rough string be suspended so that it doesn't lie in the centre of the string, meaning that the ends of the string make different angles with the horizontal and so have different tensions?
Yes, this comes up a bit in M1, where one string is longer than the other, so there's more tension in that one. They will always be at different angles to the horizontal though.

(Original post by hhattiecc)
Also, why is the tension in each part of the light string in a particle-pulley system equal?
This is only if the pulley is smooth (which it is in M1), so there is no extra friction on one side of the string, so therefore both forces in the string will be equal.

Keep in mind these only apply for strings that are taut (don't stretch, have constant length for your calculation).
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lerjj
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Both - if it's a single string it must have tension constant throughout. Otherwise you have a force gradient and the string is going . to . start . to . stretch. If you have two different strings attached then the lengths will be different so you'll have different angles and different tensions, but if you suspend a bead on a single string, it will equalise and balance in the middle.
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hhattiecc
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I see thank you both!!
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