- #1
illu45
- 5
- 0
Hello all,
This is (I think) one of the more popular introductory physics questions. Someone ties a bucket to a rope, puts some water in it and swings it around in a vertical circle with relatively constant speed. When the bucket is directly above the person's head, the water stays in the bucket. I, however, can't seem to figure out why this happens.
I've drawn the Free Body Diagram of the water a number of times, and this is what I get:
F(g) = mg [down]
F(n) [down]
Thus the centripital force is down, as it should be, into the centre of the circle.
I also drew the FBD of the bucket, here are the forces I have:
F(g)= mg[down]
T = [down]
F(c) is therefore also down.
I realize that there is a centripital velocity to the bucket, which is perpendicular to the circle. If I square this velocity, divide it by the radius (r) and the mass (m), I should get a centripital force F=ma, a=v^2/r, F=m(v^2/r).
From what I understand, this vector is parallel to the velocity (vc). However, that would also make it perpendicular to the gravitational and tension forces, meaning that it does not affect them. So, in the x-hat direction, I have this (centrifugational?) force, and in the y-hat I have the Tension and the gravitational force. However, I still cannot figure out why the water does not fall out. The forces should be orthogonal and thus there is no upwards force or any component of a force in the positivie y-hat direction to keep it up...
If someone could provide me with an explanation, I would greatly appretiate it,
Thanks,
illu45
EDIT: Appologies if the problem is somewhat muddled, I've become rather confused trying to solve it :D. I think that the description is clear enough, though...
This is (I think) one of the more popular introductory physics questions. Someone ties a bucket to a rope, puts some water in it and swings it around in a vertical circle with relatively constant speed. When the bucket is directly above the person's head, the water stays in the bucket. I, however, can't seem to figure out why this happens.
I've drawn the Free Body Diagram of the water a number of times, and this is what I get:
F(g) = mg [down]
F(n) [down]
Thus the centripital force is down, as it should be, into the centre of the circle.
I also drew the FBD of the bucket, here are the forces I have:
F(g)= mg[down]
T = [down]
F(c) is therefore also down.
I realize that there is a centripital velocity to the bucket, which is perpendicular to the circle. If I square this velocity, divide it by the radius (r) and the mass (m), I should get a centripital force F=ma, a=v^2/r, F=m(v^2/r).
From what I understand, this vector is parallel to the velocity (vc). However, that would also make it perpendicular to the gravitational and tension forces, meaning that it does not affect them. So, in the x-hat direction, I have this (centrifugational?) force, and in the y-hat I have the Tension and the gravitational force. However, I still cannot figure out why the water does not fall out. The forces should be orthogonal and thus there is no upwards force or any component of a force in the positivie y-hat direction to keep it up...
If someone could provide me with an explanation, I would greatly appretiate it,
Thanks,
illu45
EDIT: Appologies if the problem is somewhat muddled, I've become rather confused trying to solve it :D. I think that the description is clear enough, though...