Emptying a Bowl: Calculating Work

  • Thread starter Thread starter teken894
  • Start date Start date
  • Tags Tags
    Work
Click For Summary
SUMMARY

The discussion focuses on calculating the work done to empty a hemispherical bowl with a radius of 8 inches, filled with punch weighing 0.04 pounds per cubic inch, to within 2 inches of the top. The correct approach involves using the formula for work, defined as the product of force (weight) and displacement. The weight is calculated using the equation weight = (0.04)(π * r²)dx, leading to the total work being represented by the integral from 2 to 8 of (0.04π)(x)(64 - x²)dx. This method accurately accounts for the displacement and weight of the liquid being pumped over the rim.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with the concept of work in physics.
  • Knowledge of the geometry of hemispherical shapes.
  • Basic understanding of fluid mechanics and weight density.
NEXT STEPS
  • Study integration techniques for calculating work in physics problems.
  • Learn about the properties of hemispherical volumes and their applications.
  • Explore fluid mechanics principles related to weight density and buoyancy.
  • Review examples of similar problems involving work and displacement in calculus.
USEFUL FOR

Students studying calculus and physics, particularly those focusing on applications of integration in real-world scenarios involving work and fluid dynamics.

teken894
Messages
25
Reaction score
0

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?

Homework Equations




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?
 
Physics news on Phys.org
Is it being pumped from underneath so that there is free space between the liquid and the bowl?
 
Yes, that is exactly right!
 

Similar threads

How do you calculate the work required to pump water out of a hemisphere tank?
  • · Replies 1 ·
Replies
1
Views
3K
Calculating Work for Pumping Oil from a Spherical Tank
  • · Replies 3 ·
Replies
3
Views
3K
Hemispherical bowl Volume question
  • · Replies 1 ·
Replies
1
Views
4K
Centre of Mass of an empty and filled goblet
  • · Replies 11 ·
Replies
11
Views
2K
Help calculating force needed for a robot's basketball shot
  • · Replies 4 ·
Replies
4
Views
2K
Calculating Work for Pumping Liquid in a Vertical Cylindrical Tank
  • · Replies 2 ·
Replies
2
Views
3K
Calculating Work Required to Empty a Tank of Beer
  • · Replies 2 ·
Replies
2
Views
2K
Calculate Work to Drain a Hemispherical Tank
  • · Replies 1 ·
Replies
1
Views
4K
Calculating Work to Empty a Water-Filled Trough
  • · Replies 1 ·
Replies
1
Views
3K
Volume of a bowl (using variables not numbers)
  • · Replies 5 ·
Replies
5
Views
13K