Solving the Water Bucket Problem: Finding Vmin with Given Parameters"

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In summary, the question asks if it is possible to whirl a bucket of water in a vertical circle without the water falling out at the top. The minimum speed needed to achieve this is found by equating the net force on the water to its weight and using the distance from the shoulder to the bottom of the bucket as the radius of the circle. The mass of the bucket is not needed for this calculation. Additionally, at the top of the circle, the tension force exerted by the arm is equal to the weight of the water, resulting in no net force and allowing the bucket to continue in its circular motion.
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Homework Statement



Is it possible to whirl a bucket of water fast enough in a vertical circle so that the water won't fall out at the top? If the distance from your shoulder to the bottom of the bucket is 0.77 m and the water has a mass of 5.05 kg, what is the minimum speed to whirl the pail?

Homework Equations





The Attempt at a Solution



The answer is yes, but to find Vmin?

I know r = .77m, m = 5.05kg (although shouldn't I have been given the bucket mass also?), so i was thinking

Fnet = -Fg + Ft = mV^2/r

but how do i find Ft, or is there no Ft? explain
 
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  • #2
You don't need the mass of the bucket because you're concerned about the water. What do you mean by Ft? You're looking for the sum of the forces to come to equilibrium.
 
  • #3
By Ft I mean tension force exerted by my arm. I didn't think there was any Fn (normal force), right?
 
  • #4
If the bucket is swinging "just fast enough", your arm exerts no force on it at the top of the circle. With that information you can solve your equation,
Fnet = -Fg + Ft = mV^2/r
 

FAQ: Solving the Water Bucket Problem: Finding Vmin with Given Parameters"

What is the "Water Bucket problem"?

The "Water Bucket problem" is a mathematical puzzle that involves using a set of different-sized buckets to measure a specific amount of water. It is also known as the "Water Jug problem" or the "Die Hard problem" after its appearance in the 1988 film "Die Hard".

How does the "Water Bucket problem" work?

The "Water Bucket problem" typically presents a scenario where you have two or more buckets of different sizes and a specific amount of water that needs to be measured. The goal is to use the buckets to measure the exact amount of water, either by filling or emptying them in a specific order.

What is the solution to the "Water Bucket problem"?

The solution to the "Water Bucket problem" depends on the specific scenario presented. However, the general approach is to use a combination of filling and emptying the buckets in a specific order to reach the desired amount of water. There are also various mathematical formulas and strategies that can be used to solve the problem.

What are some real-world applications of the "Water Bucket problem"?

The "Water Bucket problem" has practical applications in fields such as engineering, chemistry, and physics. It can be used to optimize the use of resources, such as water or chemicals, in industrial processes. It can also be used in problem-solving and critical thinking exercises to improve cognitive skills.

Are there variations of the "Water Bucket problem"?

Yes, there are many variations of the "Water Bucket problem" that involve different numbers of buckets, different sizes of buckets, and different amounts of water. Some variations also have additional constraints, such as time limits or restrictions on the number of steps allowed. These variations can make the problem more challenging and require different strategies to solve.

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