# Centripetal motion - swinging a bucket full of water

• SA32
In summary, the bucket must have an angular speed of at least 3 rad/s in order for the water to not fall out. The force on your hand is greatest when the bucket is at the top of the path and decreases as the bucket moves down.
SA32
I'm having trouble coming up with a strategy for this problem. Any help is appreciated!

"You are swinging a bucket (mass 1.00 kg) containing 2.00 kg of water at a constant angular speed in a vertical circular path (the path lies in a vertical plane) of radius 1.00 m.

a.) What is the minimum angular speed that the bucket must have in order that the water does not fall out of the bucket at the top of its path?
b.) Assuming that you are swinging the bucket at the angular speed found in (a), what is the force on your hand due to the bucket handle (give magnitude and direction) at i.) its highest point and ii.) its lowest point?"

A
Okay, so, first let me see if I understand correctly why the water does not fall out of the bucket at the top of the path at a certain speed...

At the top of the circular path, there is a downward force of the object's weight and a downward force of my hand on the bucket. If I swing the bucket with enough force so that the magnitude of the acceleration of the bucket toward the center of rotation is greater than the magnitude of the acceleration due to gravity, the water cannot fall out because it is not accelerating as quickly as the bucket?

Then if the acceleration of the bucket is faster than the acceleration of the water, the water will not fall out. Which means what I'm looking for is the speed of the bucket so that it is accelerating just fast enough so that any slower and its acceleration would be less than the acceleration of water.

Does that mean I'm looking for when the acceleration of the bucket is equal to the acceleration of the water? If so I am not certain how to express this mathematically?

B
Really lost with this one... to increase the acceleration of the bucket I need to increase the force of my hand on the bucket. Does this mean the magnitude of the force of the bucket on my hand also increases? Again, I'm confused about how to express this mathematically.

Thanks ahead of time for any insight.

Does that mean I'm looking for when the acceleration of the bucket is equal to the acceleration of the water? If so I am not certain how to express this mathematically?

You are doing fine. Think in terms of forces, and draw a free body diagram of the bucket when it is at the highest point of the curve. If you do that, you will see the forces that need to be balanced in order to keep the water from falling down.

Really lost with this one... to increase the acceleration of the bucket I need to increase the force of my hand on the bucket. Does this mean the magnitude of the force of the bucket on my hand also increases? Again, I'm confused about how to express this mathematically.

A free body diagram will help here too. Draw one for the position of the bucket at the top of the vertical circle, (that would be the same as you used in A), and a second one for the bucket at the bottom of the circle.

If you do this, you will see that there are more forces pulling on your hand at the bottom then there are at the top. You should also be able to express this as a sum of forces, based on your diagram and of course, Newton's Second Law.

Dorothy

Figured it out, thanks!

## What is centripetal motion?

Centripetal motion is the motion of an object along a circular path, where the object's velocity is constantly changing due to the force pulling it towards the center of the circle.

## How does swinging a bucket full of water demonstrate centripetal motion?

When swinging a bucket full of water in a circular motion, the water stays in the bucket due to the centripetal force acting on it, pulling it towards the center of the circle.

## What factors affect the amount of centripetal force in swinging a bucket full of water?

The amount of centripetal force is affected by the mass of the object (in this case, the bucket and water), the speed of the object, and the radius of the circular path.

## Can centripetal motion be applied to other real-life situations?

Yes, centripetal motion is commonly observed in many real-life situations such as the motion of planets around the sun, the rotation of a Ferris wheel, and the swinging of a pendulum.

## What happens if the centripetal force is removed while swinging a bucket full of water?

If the centripetal force is removed, the water in the bucket will continue to move in a straight line tangential to the circular path, causing it to spill out of the bucket.

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