# Emptying a Bowl: Calculating Work

• teken894
In summary, the conversation is about finding the amount of work done when emptying a hemispherical bowl filled with punch, given the radius and weight of the punch. The approach to solving the problem involves calculating the weight and displacement, and then using integration to find the total work. The clarification is also provided that the contents are pumped from underneath, leaving a space between the liquid and the bowl.
teken894

## Homework Statement

A hemispherical bowl with radius 8-inches is filled with punch (weighing .04 pound/in^3) to within 2-inches of the top. How much work is done emptying the bowl if the contents are pumped just high enough to get over the rim?

## The Attempt at a Solution

Work = Force(weight)* displacement.

i said displacement was "x"
and for the weight:
r = sqrt(64- x^2)
weight = (.04) (pi * r^2)dx

and so, work to lift weight at a given "x"
is weight*displacement

so i get total work is

integration from 2 to 8 of

(.04pi)(x)(64 - x^2)dx

Is this the right way to approach this problem?

Is it being pumped from underneath so that there is free space between the liquid and the bowl?

Yes, that is exactly right!

## 1. How do you calculate the work done in emptying a bowl?

The work done in emptying a bowl can be calculated by multiplying the weight of the bowl by the distance it is lifted. This is known as the work-energy principle, which states that the work done is equal to the change in energy of the object.

## 2. Does the shape of the bowl affect the amount of work done?

Yes, the shape of the bowl can affect the amount of work done. A wider and shallower bowl will require less work to empty compared to a taller and narrower bowl, as the weight and distance lifted will be less.

## 3. How does the weight of the bowl impact the amount of work done?

The weight of the bowl is directly proportional to the amount of work done. This means that the heavier the bowl, the more work is required to lift it and empty its contents.

## 4. Is the work done in emptying a bowl the same as the force applied?

No, the work done and the force applied are not the same. Work is a measure of energy transfer, while force is a measure of the push or pull on an object. The work done in emptying a bowl takes into account the distance the bowl is lifted, while force does not.

## 5. Can the work done in emptying a bowl be negative?

Yes, the work done can be negative if the bowl is being lowered rather than lifted. In this case, the energy is being transferred from the bowl to the surface it is being placed on, resulting in a negative work value.

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