Newtonian Mechanics – Why Is the Net Work Done in a Pulley-String System Zero?

Question

In any pulley system, where the pulleys and strings are massless and frictionless, why is the net work done by Tension zero?

Answer 1

In the systems you describe, each string connects always two masses. The tension force exerted on these two masses by the string is equal in magnitude and opposite in direction with respect to the displacement. Hence, the work done by each string on the two masses attached have opposite sign. As a consequence, if you sum up all contributions from each string and each mass, the net work done by tension is zero.