Question

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?

Answer 1

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:
$mg-2T=0$
so
$mg=2T$
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
$mg=2\cdot 90.5 N= 181 N$

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
$mg-T=0$
and so, since we know from part a) that $mg=181 N$, we can find the new tension T:
$T=mg=181 N$