Part a of the drawing shows a bucket of water suspended from the pulley of a well; the tension in the rope is 90.5 n. part b shows the same bucket of water being pulled up from the well at a constant velocity. what is the tension in the rope in part b?

Missing figure in the problem: https://www.physicsforums.com/attachments/p4-46-gif.117834/

Solution:

part a) The bucket is not moving so the resultant of the forces acting on it is zero. Let's apply the equation of equilibrium. We have:

so

where T=90.5 N is the tension of the rope, and a factor 2 is applied because the string holds the bucket twice. From this we find


part b) Here the situation is different: the string holds the bucket only in one point. Moreover, the bucket is pulled up at constant velocity, so zero acceleration: this means that the resultant of the forces acting on the bucket is zero. Therefore, the equation of equilibrium in this case is

and so, since we know from part a) that , we can find the new tension T: