00:01
So in this problem we are given a situation where there is a string attached to the wall at this point and it has a fixed pulley which has a mass m2 of 87 kgis given over here and in the middle of this string there is a freely moving pulley which is on the line on string with the mass of 12 kgis and we are supposed to find the theta value for which the system is in static equilibrium so before we solve anything we need to deduce a couple of things from this diagram.
00:38
The first thing is that the tension in these strings is all equal.
00:46
We are given that the pulleys are frictionless and we also assume that the pulle is massless as well.
00:52
Because if that's the case if you draw a free body diagram of let's say the first fixed pulley, there is a tension t over here and there is a tension t over here and let's say there were t1 and t2.
01:04
And so the moments about the center of this pulley have to be balanced.
01:10
So t1 times r should be equal to t2 times r given the radius of the pulley.
01:16
And so these tensions must be equal to zero, must be equal in this case.
01:21
And the same argument goes for the next pulley as well because they're not moving and there is no angular acceleration or friction force that can explain the difference in these two talks.
01:32
So with this argument we say that the tension, all these strings are the same...