Really (neccessarily) quick M4 question

When you have a particle 'attached to the midpoint' of a string (seems to a fairly common question) and the string is extended, what governs the tension both sides of the particle, and is it constant.

say a string of natural length 'l' is stretched to 2l, modulus lambda and a particle attached to its midpoint, what is the tension both sides?

thanks

Reply 1

Greg88

hai2410

If the particle isn't weighless, then the tension will not be constant. Assuming it's attached to the midpoint before extension, then you would have to solve the problem by looking at the extension of each half and then balancing the tension either side.

i.e.
extension in top + extension in bottom = total extension
tension in top = tension in bottom + force due to weight

Then equate the tensions to extensions and solve simultaneously for tension. Or at least that's how I'd solve it, though there may be other methods.