# Bucket in Rotation Problem

• dark_elf
In summary, the conversation discusses a problem involving a bucket of water being swung in a vertical plane at the end of a rope. The mass and length of the rope are given, and the gravitational acceleration is assumed to be 10 m/s2. Two questions are posed: the minimal speed of the bucket to prevent the water from falling out, and the magnitude of the centripetal acceleration experienced by the water at the highest point. Equations for acceleration in circular motion are mentioned, but the person asking for help is unsure of how to start solving the problem.

## Homework Statement

A bucket of water is swung in a vertical plane at the end of a rope of length l= 6 m. The mass of the bucket plus water is 5 kg and the gravitational acceleration is g=10 m/s2. We assume that the mass of the rope can be neglected.

(a) What is the minimal speed of the bucket at its highest point in the circular motion, such that the water does not fall out? (in m/s)

(b) For this speed, what is the magnitude of the centripetal acceleration that the water in the bucket experiences at the highest point? (in m/s2)

## Homework Equations

ω = ω0 + α * t
θ = ω0 * t + 0.5 * α * t ^ 2
ω = ω0 ^ 2 + 2 * α * θ

## The Attempt at a Solution

I am newbie in physics, I solved some problems in kinematics already, but I don't even know how to start in this case

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To solve this problem, you need an equation for acceleration in circular motion. Do you have it?

@dark_elf, You should not ask for solution of this question. It's a breach of honor code you accepted at 8.01x course.

## 1. What is the "Bucket in Rotation Problem?"

The Bucket in Rotation Problem is a physics problem that involves a bucket of water attached to a string being swung in a circular motion. The goal is to determine the minimum velocity required for the water to stay in the bucket as it moves in a vertical circle.

## 2. What are the key factors that affect the Bucket in Rotation Problem?

The key factors that affect the Bucket in Rotation Problem are the mass of the bucket, the length of the string, the mass of the water in the bucket, and the speed of rotation.

## 3. How does the centripetal force affect the Bucket in Rotation Problem?

The centripetal force, which is the force that keeps the bucket moving in a circular path, is crucial in the Bucket in Rotation Problem. It is responsible for keeping the water in the bucket as it moves in a vertical circle.

## 4. Can the Bucket in Rotation Problem be applied to real-life situations?

Yes, the Bucket in Rotation Problem has real-life applications in fields such as amusement park rides, engineering, and sports. It helps engineers determine the minimum speed and strength required for a ride to safely keep riders in their seats, and also helps athletes understand the physics behind certain movements in sports such as gymnastics.

## 5. How can the Bucket in Rotation Problem be solved?

The Bucket in Rotation Problem can be solved by using the equation for centripetal force, Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the water, v is the velocity, and r is the radius of the circular motion. By setting Fc equal to the weight of the water, mg, and solving for v, the minimum velocity required to keep the water in the bucket can be determined.