A small sphere of mass falls from rest through a viscous fluid that exerts a linear…

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Kinematics and Newtonian dynamics of particles · Lagrangian mechanics

Action and Symmetry, Ch Multipliers, non-holonomic constraints and forces outside the potential

Problem

A small sphere of mass

0.050\,\mathrm{kg}

falls from rest through a viscous fluid that exerts a linear drag force

-b\mathbf{v}

with

b = 0.015\,\mathrm{kg\,s^{-1}}

. The Rayleigh dissipation function for this drag is

\mathcal{F} = \tfrac12 b v^2

. ((a)) Find the terminal speed

v_{\rm t}

. ((b)) Evaluate

2\mathcal{F}

v = v_{\rm t}

and compare it with the rate

mgv_{\rm t}

at which gravity does work on the sphere at that speed.

Related theory

Lagrangian mechanics

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