Resources

Modeling Scenario

1-105-AnimalFall-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: animal Netwon's Second Law of Motion falling body terminal velocity air resistance Newton air friction fall

192 total view(s), 86 download(s)

Abstract

Resource Image This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

Citation

Researchers should cite this work as follows:

Article Context

Description

The following is a problem from Hobbie, Russell K. and Bradley J.Roth. 2007. Intermediate Physics for Medicine and Biology, Fourth Edition. New York: Springer Science and Business Media, p. 45, Exercise 28.When an animal of mass m falls in air, two forces act on it: gravity, m*g, and a force due to air friction. Assume that the frictional force is proportional to the speed v.

  1. Write a differential equation for v based on Newton' s second law, F = m (dv/dt).
  2. Solve this differential equation.
  3. Assume that the animal is spherical, with radius a and density rho. Also, assume that the frictional force is proportional to the surface area of the animal. Determine the terminal speed (speed of descent in steady state) as a function of a.
  4. Use your result in part (c) to interpret the following quote by J.~B.~S.~Haldane ``You can drop a mouse down a thousand - yard mine shaft; and arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.''
  5. Added: Offer any comments on how a given animal may mitigate or at least reduce this terminal velocity.

Article Files

Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Comments

Comments

There are no comments on this resource.