Imagine a massless and frictionless pulley with two weights hanging either side of the pulley by a massless string.
Like this except not attached to a ceiling
Rather than being fixed to a ceiling, the pulley is being pulled upward by an external force F, with the weights and string still attached.
Due to Newton's 2nd Law,
ΣFy=F−2T=ma,
where T is the tension in the string on either side of the pulley and a is the vertical acceleration of the pulley.
Clearly, since there is a net upward force, the pulley itself will accelerate upwards.
But because the m=0,
F−2T=0.
Does this not then suggest that the pulley has a constant velocity?
Answer
In the equation Fnet=ma, normally we would assume that Fnet=0 implies a=0 on the right-hand side. However, for a massless object, we can satisfy the equation by having Fnet=0, m=0, and a≠0. In reality, of course, the pulley is not massless, so m is small, a is some nonzero number, and Fnet is small.
The above reasoning is the justification for the usual assumption that low-mass objects transmit forces unchanged, e.g., that the tension in a rope is the same value throughout the length of the rope.
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