9846

Buoyancy, Gravity, and Drag on a Sphere Immersed in a Liquid

This Demonstration shows the velocity and position as functions of time for two spheres immersed in a liquid, rising under the influence of the forces of buoyancy, gravity, and drag. You can vary the base mass and radius of the blue sphere, and also the red sphere's mass and radius relative to the blue sphere. The spheres start out at the bottom, defined as 0 meters on the scale, and travel upward to a height of 100 meters, where they will have achieved terminal velocity.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The motion is described by the force equation:
.
The forces are due to gravity, buoyancy, and drag, which appear in that order in the above differential equation. The Demonstration restricts the controls to make certain that the spheres are buoyant. The buoyant force acts upward, while gravity acts downward, as does the drag, which acts as a retarding force proportional to the square of the velocity. When the upward and downward forces reach equilibrium, a terminal velocity is attained.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+