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First of all i have a question regarding a simple Atwood's machine. The pulley has no mass and the string has no mass and is inextensible. If one pulley is suspended from a fixed support and it has 2 masses ; one at either end of the string. If i construct a free-body diagram of the pulley it has 2 forces directed upwards , both being the tension T. So as the pulley does not move , that means there must be a force of 2T acting downwards which is the force that the pulley exerts on the fixed support. If the pulley is suspended by a string , shouldn't the tension 2T be acting upwards ?

If the string suspending the pulley is now cut and the system goes into free-fall ; what does the free-body diagram look like for the massless pulley ?I have that the tension T is now zero so there are no forces acting upwards , but the pulley has no mass so has no weight. So , there are no forces on it , yet it is accelerating downwards ?

Thanks