A ball is thrown straight up into air that exerts quadratic drag

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 ball is thrown straight up into air that exerts quadratic drag, with yy measured upward and drag always opposing the instantaneous velocity: mv˙=−mg−bv∣v∣,m\dot v = -mg - bv|v|, with b>0b > 0 in kg m−1\mathrm{kg\,m^{-1}}. The ball has mass m=0.15 kgm = 0.15\,\mathrm{kg} and drag constant b=0.0050 kg m−1b = 0.0050\,\mathrm{kg\,m^{-1}}, and is released at y0=0y_0 = 0 with upward velocity v0=15 m s−1v_0 = 15\,\mathrm{m\,s^{-1}}. Air resistance is the only force besides weight. (a) Write the acceleration a(v)=−g−(b/m)v∣v∣a(v) = -g - (b/m)v|v| and the update rule (velocity from the acceleration, then position from the velocity already held before the step). (b) Hand-compute v1v_1, y1y_1 after one step of Δt=0.20 s\Delta t = 0.20\,\mathrm{s}, then v2v_2, y2y_2 after a second step of the same size, recomputing the drag term each time. Use g=9.81 m s−2g = 9.81\,\mathrm{m\,s^{-2}}.

Browse the problem library