I learnt about the derivation of the shape of water in a spinning (constant speed) bucket. It's a parabola, however the explanations all assume the net force (centripetal/centrifugal and gravity) is perpendicular to the surface or equivalently state that these 3 forces (perp, grav and cent) must cancel, without considering the tangential forces? Why must the net force be perpendicular and why do no net tangential forces exist in a spinning water of bucket?
Why must the net force on the surface of water spinning in a bucket be perpendicular to the surface?
Add a comment
|
3 Answers
$\begingroup$
$\endgroup$
At first, the tangential force from the bucket wall makes the water element in contact accelerate. The inner elements are then accelerated by the outer ones.
However, once the system rotates at a constant angular velocity, there are no tangential forces between that layers because there are no relative movement.
Solids support static shear stresses, that is why we must take in consideration the static friction between the tires and the ground in a car rotating around an inclined lane. Liquids flow under shear stresses and the notion of static friction doesn't apply to them.
answered Sep 18 at 20:47
$\begingroup$
$\endgroup$
The water in the bucket forms a parabola because the net forces(centripetal/centrifugal and gravity) must be perpendicular to the surface to keep it equilibrium. There are no tangential forces as, if there will be the water will not be in a single shape(it will keep changing the shape), until equilibrium is restored.
Thank you
$\begingroup$
$\endgroup$
In a spinning bucket filled of water, there is no tangential force acting on the water. The rotation of the water is just a consequence of conservation of angular momentum: once it has started rotating and reached an equilibrium with itself and the sides of the bucket there is no need for an external force to keep it in motion. As if it were a rigid body that keeps rotating on its own. If you stopped the bucket the water would keep spinning for a while, but here a tangential force would originate at the interface water-bucket leading it to a stop after some time.
When you think about the forces, you need to be cautious about the frame of reference you are considering. From the point of view of an experimenter observing the bucket, the net force acting on a small volume of water (gravity and pressure from the neighboring water) won't be perpendicular to the surface, but point directly to the axis of rotation, because the water is accelerating inward (circular motion). From the non-inertial rotating frame of reference, in which the bucket and water are at rest, the forces (gravity, water pressure reaction, centrifugal) must cancel exactly. But because the reaction of the water beneath a given volume of water points directly toward the surface and it's perpendicular to it, it follows the sum of gravity and centrifugal must cancel it and be themselves perpendicular to the surface.
The reaction of the water is perpendicular to the surface for the same reason the reaction of the table on a ball resting on it is perpendicular to the surface of the table. If there were tangential forces the object (the water) would move and not stay at rest.
