Rotating Pail of Water

In summary, to find the shape of the surface of a rotating pail of water with an angular velocity w, the slope of the surface must be resolved to find tan(theta) as a function of x. Once this is known, the height of the outer edge can be solved for as a function of x. The pail, rotating at a rate of once per second with a diameter of 0.45 m, can be solved using the assumption that the centre of the water surface is the origin and that the tangential force is zero.
  • #1
Fusilli_Jerry89
159
0

Homework Statement


A rotating pail of water with an angular velocity w has a surface curving up from the centre to the outer edge. Find the shape of the surface. The slope of the surface is dy/dx = tan(theta) at position x is y (= function of x) is the shape of the surface. You must resolve forces to find tan(theta) as a function of x, and then solve for the height, y, as a function of x.

If the pail rotates once per second, and has a diameter of 0.45 m, how high above the centre is the outer edge?



Homework Equations





The Attempt at a Solution


All I see is that w = 2pi rad/sec and r = 0.225 m.
 
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  • #2
Method I:
Ideal Fluid, by definition, can not tolerate any shear force. Use this fact.
Assume the centre of the water surface to be origin. Let P(x,y) be a point on the water surface. Consider forces on it. Impose the condition that tangential force will be zero.
I hope you can proceed now.
 
  • #3
I am not sure what the rest of the information is asking for. I would need more information about the pail and the forces acting on it to accurately determine the shape of the surface. Additionally, the given equations and attempt at a solution are not applicable to this problem as they do not provide enough information. Can you please provide more details about the pail and the forces involved?
 

1. What is a rotating pail of water?

A rotating pail of water is a scientific demonstration in which a pail filled with water is spun rapidly in a circular motion. This causes the water to stay inside the pail, defying gravity, due to the centrifugal force created by the rotation.

2. How is a rotating pail of water created?

To create a rotating pail of water, a pail or bucket is filled with water and then spun rapidly in a circular motion. This can be done manually or with the help of a motor or rotating platform.

3. What causes the water to stay inside the pail?

The water stays inside the pail due to the centrifugal force created by the rotation. This force acts in an outward direction, causing the water to push against the sides of the pail, creating a barrier that keeps it inside.

4. What happens if the rotation is stopped suddenly?

If the rotation is stopped suddenly, the centrifugal force will also stop, causing the water to fall out of the pail. This is because there is no longer an outward force pushing against the water, so gravity takes over and pulls it down.

5. What is the purpose of a rotating pail of water in science?

A rotating pail of water is used in science demonstrations to showcase the effects of centrifugal force and the concept of rotational motion. It is also used to explain how objects can defy gravity and stay in place when experiencing circular motion.

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