Apiano mover raises a 1000-n piano at a constant speed using a very light rope in a frictionless pulley system, as shown in the figure. with what force is the mover pulling down on the rope?

Here As we can see the figure that the end of the rope is pulled by some force F

Now as we can see that Piano is connected by a pulley which is passing over the pulley so effectively net force on the piano upwards will be 2F as it is connected by 2 ropes by the pulley

Now for constant velocity of the piano we will say

since velocity is constant so acceleration must be ZERO

so here we have

as we know here that

mg = 1000 N

so we will have

so here force must be 500 N

no. dot product   =0 when vecs at right angles

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