Circular motion of a bucket filled with water

In summary, when a bucket filled with water is in vertical circular motion, there exists a contact force between the water and the bucket at the top of the center of rotation. This is because the bucket is accelerating downwards at more than 1g, providing a centripetal force to constrain the water to move in a circular path. If the bottom part of the bucket is removed while at the top, the water will leave through the bottom and travel on a tangential path, as if any mass were being swung on a string in a vertical plane. The contact force will be at least twice the weight of the water if the rotation is uniform. When doing a force balance on the water in the bucket, the equation R+mg=mv
  • #1
Faiq
348
16
Consider a bucket filled with water in vertical circular motion.
Why does there exist a contact force between water and the bucket when the bucket is at the top of center of rotation?
What will happen if I remove the bottom part of the bucket when it is on the top?
 
Physics news on Phys.org
  • #2
Faiq said:
Why does there exist a contact force between water and the bucket when the bucket is at the top of center of rotation?
Because the bucket accelerates downwards at more than 1g.
Faiq said:
What will happen if I remove the bottom part of the bucket when it is on the top?
What do you think?
 
  • #3
The water will leave through the bottom and travel (as the theory always tells us) on a tangential path. This is exactly the same as if any mass were being swung on a string in vertical plane and going fast enough to be kept in a circle. Naturally, there are practicalities involved with actually getting all the water to leave at once and, in reality, there would be a 'fan' of water out of the bottom, each bit would be tangential to the path of the bucket.
There exists a contact force between bucket and water because the bucket is providing a centripetal force to constrain the water to move in a circular path. It has to be going fast enough to have a centripetal acceleration of at least g, for the bucket to 'overtake' the Earth's gravitational acceleration of g downwards and still be 'pressing inwards' on the water. At the bottom, the contact force will be at least twice the weight of the water, if the rotation is uniform.
 
  • #4
A.T. said:
Because the bucket accelerates downwards at more than 1g.

What do you think?
How do you make up the assumption that acceleration is greater than g. Isn't it possible that the reaction force cancels some of the weight leaving the centripetal acceleration smaller than g?
 
  • #5
Faiq said:
How do you make up the assumption that acceleration is greater than g.
Well, try to rotate it slower and report back.
 
  • Like
Likes rollete and sophiecentaur
  • #6
Faiq said:
Consider a bucket filled with water in vertical circular motion.
Why does there exist a contact force between water and the bucket when the bucket is at the top of center of rotation?
What will happen if I remove the bottom part of the bucket when it is on the top?
What do you get if you do a force balance on the water in the bucket?
 
  • #7
Chestermiller said:
What do you get if you do a force balance on the water in the bucket?
R+mg = mv^2/r
 
  • #8
Faiq said:
R+mg = mv^2/r
Excellent. So this is the equation that applies at the moment that the bucket is directly overhead. What can you conclude from this equation?
 
  • #9
Many things can be concluded. What are we emphasizing on?
 
  • #10
Faiq said:
Many things can be concluded. What are we emphasizing on?
Conclusions related to the questions you asked.
 
  • #11
Well if you're hinting about the reaction force then we can conclude that
R = mv^2/r - mg
 
  • #12
Faiq said:
Well if you're hinting about the reaction force then we can conclude that
R = mv^2/r - mg
So what does that tell you?
 
  • #13
Well it tells me that as long as v^2/r > g, there will be a reaction force. If v^2/r = g then reaction force will be 0
 
  • #14
Faiq said:
Well it tells me that as long as v^2/r > g, there will be a reaction force. If v^2/r = g then reaction force will be 0
Excellent!

Now, if there were a small hole in the bottom, would water spray out if the inequality applied?
 
  • #15
No because centripetal acceleration is moving the water towards itself more as compared to gravity.
 
  • #16
Faiq said:
No because centripetal acceleration is moving the water towards itself more as compared to gravity.
But the reaction force tells you that there is fluid pressure at the bottom of the bucket. The pressure is equal to the reaction force divided by the cross sectional area of the bucket.
 
  • #17
How about when v^2/r = g. What will happen to reaction force then?
 
  • #18
Faiq said:
How about when v^2/r = g. What will happen to reaction force then?
It would be zero(as you said), and the fluid pressure at the bottom would be zero(gauge). So the water would be in free fall, and none would spray out the hole.
 
  • #19
Okay one more thing, if the tangential velocity is towards the right at top. The water must be pushed from the left side of the bucket. Wouldn't that give rise to a reaction from the left side?
 
  • #20
Faiq said:
Okay one more thing, if the tangential velocity is towards the right at top. The water must be pushed from the left side of the bucket. Wouldn't that give rise to a reaction from the left side?
Is the tangential velocity constant?
 
  • #21
Direction is changing so no
 
  • #22
Faiq said:
Direction is changing so no
Direction is changed by the centripetal force, not by tangential forces.
 
  • #23
Faiq said:
Direction is changing so no
So, if it is not accelerating tangentially, the sides of the bucket do not have to apply sideways force as the bucket passes overhead.
 
  • #24
Chestermiller said:
So, if it is not accelerating tangentially, the sides of the bucket do not have to apply sideways force as the bucket passes overhead.
Oh okay, got it thank you very much. If the bucket was connect through an extensible string, would there be an angular acceleration, if the motion was vertical? If no, can you give me a case where there is an angular acceleration?
 
  • #25
Faiq said:
If no, can you give me a case where there is an angular acceleration?
It's your scenario. You simply say that you accelerate it angularly with your arm.
 
  • #26
Faiq said:
Oh okay, got it thank you very much. If the bucket was connect through an extensible string, would there be an angular acceleration, if the motion was vertical? If no, can you give me a case where there is an angular acceleration?
It is not very clear what you mean by this.

Possibly you imagine a bucket in motion in a not-quite-circular path in a vertical plane. It is restrained by a bungee cord rather than by a string. The bungee stretches at the bottom portion of the path and retracts on the upper portion. But at the top and bottom of the arc, there is still no tangential acceleration -- the bungee is at right angles to the trajectory and is neither stretching further nor retracting further.

Possibly you imagine that a string is being reeled in (or payed out). Because of this, the path of the bucket as it passes overhead is not horizontal. There is an angular acceleration as a result.

Or you can use an inextensible string. Just move your hand in a circle that "leads" the bucket by 90 degrees so that the string tension has both a component radial to the bucket's path and a non-zero component that is tangential. (This hand motion is very natural - you do it automatically without even thinking about it). Now, as the bucket passes directly overhead, the string is still accelerating it.
 
  • #27
jbriggs444 said:
It is not very clear what you mean by this.

Possibly you imagine a bucket in motion in a not-quite-circular path in a vertical plane. It is restrained by a bungee cord rather than by a string. The bungee stretches at the bottom portion of the path and retracts on the upper portion. But at the top and bottom of the arc, there is still no tangential acceleration -- the bungee is at right angles to the trajectory and is neither stretching further nor retracting further.

Possibly you imagine that a string is being reeled in (or payed out). Because of this, the path of the bucket as it passes overhead is not horizontal. There is an angular acceleration as a result.

Or you can use an inextensible string. Just move your hand in a circle that "leads" the bucket by 90 degrees so that the string tension has both a component radial to the bucket's path and a non-zero component that is tangential. (This hand motion is very natural - you do it automatically without even thinking about it). Now, as the bucket passes directly overhead, the string is still accelerating it.
I was concerned with the angular acceleration. Not the tangential acceleration.
 
  • #28
When there is a vertical motion with an object connected to the centre by an extensible string, there are varying magnitudes of tension at each point because of the change in centripetal force. What I am asking is whether this situation could give rise to an angular acceleration?
 
  • #29
Faiq said:
I was concerned with the angular acceleration. Not the tangential acceleration.
Can you explain the distinction you see between the two? There is a distinction that can be made, but the relevance escapes me.
 
  • #30
Angular acceleration is change in angular velocity with respect to time. Tangential acceleration is change in linear velocity with respect to time.
 
  • #31
Does anyone else besides me feel like this thread is going down the rabbit hole?
 
  • Like
Likes jbriggs444
  • #32
Faiq said:
When there is a vertical motion with an object connected to the centre by an extensible string, there are varying magnitudes of tension at each point because of the change in centripetal force. What I am asking is whether this situation could give rise to an angular acceleration?
What do you mean by an "extensible string"? Do you still envision a circular path? Do you still envision a circular path centered on the attachment point of the string? Where along the path do you expect angular acceleration to occur?
 
  • #33
jbriggs444 said:
What do you mean by an "extensible string"? Do you still envision a circular path? Do you still envision a circular path centered on the attachment point of the string? Where along the path do you expect angular acceleration to occur?
What I mean by an extensible string is the amount of tension in the string is significant enough to cause an extension which will result in varying values of radius. As a result, an elliptical motion will be generated.
I want to know whether at any point will angular acceleration occur in such a case.
 
  • #34
Faiq said:
What I mean by an extensible string is the amount of tension in the string is significant enough to cause an extension which will result in varying values of radius. As a result, an elliptical motion will be generated.
I want to know whether at any point will angular acceleration occur in such a case.
You have not specified how the central force varies with string extension. That affects string length which, in turn, affects angular velocity and angular acceleration. Chet seems to have the right idea. There is little point in pursuing this line of inquiry.
 
  • #35
This problem has gotten way too complicated way too fast. It violates the three most important rules about modeling:

1. Keep it simple
2. Keep it simple
3. Keep it simple

Because of inexperience, @Faiq has greatly underestimated the complexity of a problem with a (deformable) fluid in the bucket (which would involve complicated fluid mechanics inside the bucket) and an elastic rope. So we need to take some steps back. Let's start out by analyzing the following two simpler problems:

1. A rigid mass attached to an inextensible string moving in a circle. The bucket is replaced by the rigid mass. The center of the circle remains fixed and dissipative effects are negligible. So the motion will go on forever. What is the tangential velocity of the mass as a function of angle above the horizontal if the velocity of the mass at the top of the arc is V? What is the tangential acceleration of the mass as a function of the angle?

2. Same as problem 1, except with a string that obeys Hooke's law.

Go to it @Faiq.

Chet
 
  • Like
Likes jbriggs444
<h2>1. What is circular motion?</h2><p>Circular motion is the movement of an object along a circular path. It involves a continuous change in direction, but the speed of the object remains constant.</p><h2>2. How does a bucket filled with water move in circular motion?</h2><p>A bucket filled with water will move in circular motion if it is swung around in a circular path. The water inside the bucket will also move in a circular path due to the centrifugal force created by the rotation.</p><h2>3. What is the role of centrifugal force in circular motion of a bucket filled with water?</h2><p>Centrifugal force is the outward force that acts on an object moving in a circular path. In the case of a bucket filled with water, the centrifugal force is responsible for keeping the water in the bucket as it moves in a circular motion.</p><h2>4. How does the speed of the bucket affect the circular motion of the water inside?</h2><p>The speed of the bucket affects the circular motion of the water inside in two ways. Firstly, a higher speed will create a stronger centrifugal force, causing the water to move in a wider circular path. Secondly, a higher speed will also cause the water to rise up the sides of the bucket due to the inertia of the water.</p><h2>5. What happens to the water inside the bucket when the circular motion stops?</h2><p>When the circular motion stops, the centrifugal force acting on the water also stops. This causes the water to move in a straight line, resulting in the water spilling out of the bucket. The water will continue to move in a straight line until it is affected by another force, such as gravity.</p>

1. What is circular motion?

Circular motion is the movement of an object along a circular path. It involves a continuous change in direction, but the speed of the object remains constant.

2. How does a bucket filled with water move in circular motion?

A bucket filled with water will move in circular motion if it is swung around in a circular path. The water inside the bucket will also move in a circular path due to the centrifugal force created by the rotation.

3. What is the role of centrifugal force in circular motion of a bucket filled with water?

Centrifugal force is the outward force that acts on an object moving in a circular path. In the case of a bucket filled with water, the centrifugal force is responsible for keeping the water in the bucket as it moves in a circular motion.

4. How does the speed of the bucket affect the circular motion of the water inside?

The speed of the bucket affects the circular motion of the water inside in two ways. Firstly, a higher speed will create a stronger centrifugal force, causing the water to move in a wider circular path. Secondly, a higher speed will also cause the water to rise up the sides of the bucket due to the inertia of the water.

5. What happens to the water inside the bucket when the circular motion stops?

When the circular motion stops, the centrifugal force acting on the water also stops. This causes the water to move in a straight line, resulting in the water spilling out of the bucket. The water will continue to move in a straight line until it is affected by another force, such as gravity.

Similar threads

Replies
2
Views
672
Replies
6
Views
1K
Replies
32
Views
10K
Replies
15
Views
2K
Replies
23
Views
1K
Replies
6
Views
1K
Replies
6
Views
2K
Replies
15
Views
3K
Replies
3
Views
1K
Back
Top