Gravitational Potential Energy of Liquid: Why Does It Increase?

  • Context: Undergrad 
  • Thread starter Thread starter zorro
  • Start date Start date
  • Tags Tags
    Liquid
Click For Summary

Discussion Overview

The discussion centers on the gravitational potential energy of a non-viscous liquid and why it increases continuously when a body falls through it. Participants explore the theoretical implications and mathematical expressions related to this phenomenon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions why the gravitational potential energy of the liquid increases continuously as a body falls through it.
  • Another participant suggests that the increase is due to the liquid rising as the body falls.
  • A clarification is made regarding the continuous nature of the increase in potential energy.
  • A detailed explanation is provided involving the center of mass of the liquid, particularly in the context of a vertical tube and a cylindrical plug.
  • One participant expresses difficulty in deriving the expression for the center of mass and requests hints on how to proceed.
  • Another participant outlines a method to find the necessary variables and steps to derive the center of mass, suggesting a systematic approach to the problem.
  • A later reply indicates that the participant successfully understood the explanation provided.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the derivation of the center of mass, as one participant struggles with the expression while another provides guidance. The discussion remains open-ended regarding the mathematical details.

Contextual Notes

Participants express varying levels of understanding and comfort with the mathematical derivations involved, indicating potential limitations in their assumptions or approaches to the problem.

Who May Find This Useful

This discussion may be useful for individuals interested in gravitational potential energy, fluid dynamics, and mathematical modeling in physics.

zorro
Messages
1,378
Reaction score
0
Why does the gravitational potential energy of a non-viscous liquid increase when a body falls through it?
 
Physics news on Phys.org
Because as the body falls the liquid rises.
 
I missed a word in the question. Why does it increase continuously?
 
The center of mass of the liquid increases continuously as the body sinks through the liquid.

Consider a vertical tube of water and a cylindrical "plug" that is just barely smaller diameter than the cylinder so that you can neglect the water next to the plug and just consider the water above and below the plug. It is then fairly easy to derive an expression for the center of mass of the water as a function of the height of the plug and see that it increases continuously as the plug sinks.

If you need help, I will be glad to walk you through it.
 
I tried finding out the expression but didn't get through. I am ending up with many variables. Can you give some hints?
 
Why don't we say that A is the area of the cylinder, H is the height of the column of fluid without the plug, and h is the height of the plug, d is the distance from the bottom of the column to the bottom of the plug, and p is the density of the fluid. That is all of the variables that you need to determine the height of the center of mass.

First, split the fluid into a cylinder above the plug and a cylinder below the plug. Second, find the mass of each cylinder, m1 and m2, in terms of the above variables. Third, find the height of the center of each cylinder, h1 and h2, in terms of the above variables. Fourth, write the center of mass in terms of the above variables (eliminating m1, m2, h1, and h2).

If you get stuck on any of the steps let me know.
 
I got it perfectly. Thank you very much!
 

Similar threads

High School Pressure in a viscous liquid versus non-viscous fluids
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Why does external pressure on a liquid increase vapor pressure
  • · Replies 31 ·
2
Replies
31
Views
12K
Graduate Gravitational potential energy -- Why is it always negative?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Intuition problem about an accelerating barometer
  • · Replies 33 ·
2
Replies
33
Views
2K
High School Study of SHM of an object attached to a vertical spring
  • · Replies 7 ·
Replies
7
Views
1K
High School Gravitational potential energy question -- Ojbect sitting on the Earth
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Force on a rigid body inside a liquid flow
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad How to interpret this definition of potential energy?
  • · Replies 10 ·
Replies
10
Views
2K
High School Can energy be decomposed?
  • · Replies 2 ·
Replies
2
Views
2K
High School Conceptually understanding change in potential energy with 0 net work
  • · Replies 9 ·
Replies
9
Views
2K