A pebble of mass falls through gusty air on the end of a light tether that adds a…

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Mechanics & Dynamical Systems · Kinematics and Newtonian dynamics of particles

Computational Physics, Ch A falling body that knows about air: the first simulation

Problem

A pebble of mass m=0.080 kgm = 0.080\,\mathrm{kg} falls through gusty air on the end of a light tether that adds a small drag proportional to speed on top of the usual quadratic drag. Taking vv positive downward, its equation of motion is mv˙=mg−bv2−cv,m\dot v = mg - bv^2 - cv, with b=0.00060 kg m−1b = 0.00060\,\mathrm{kg\,m^{-1}} and c=0.0020 kg s−1c = 0.0020\,\mathrm{kg\,s^{-1}}. (a) Set v˙=0\dot v = 0 and show that the terminal speed satisfies bv∞2+cv∞−mg=0bv_\infty^2 + cv_\infty - mg = 0, then solve for v∞v_\infty (take the positive root). (b) Evaluate v∞v_\infty for the numbers above, to three significant figures.

Browse the problem library