radius of steel ball = 20.0x10-3 m R density of steel ball = 7800 kg.m-3 mass of table tennis ball = 12.70x10-3 kg m drag coefficient = 0.445 CD density of air F = 1.225 kg.m-3 viscosity of air F = 1.789x10-5 Pa.s max time = 3.00 s tMax No. time steps = 10000 N Output parameters table tennis ball steel ball free fall = 0 Fdrag terminal velocity [m.s-1] 8.79 86 vT = 3.00 s [m.s-2] 0.049 8.75 9.80 t a = 3.00 s [m] 20.9 43.3 44.1 t x = 3.00 s [m.s-1] 8.77 28.3 29.4 t v = 3.00 s Reynolds number 7.8x104 t NR It is that heavier objects do fall faster than lighter ones. “true” table tennis ball steel ball Example A falling skydiver mscript mec_drag.m We can model a falling skydiver falling from rest using the numerical approach where the resistive force or drag force is Input parameters radius (estimate) = 0.500 m R mass = 70 m kg mass entered and not calculated from density drag coefficient = 0.5 CD density of air F = 1.225 kg.m-3 viscosity of air F = 1.789x10-5 Pa.s max time = 20.00 s tMax No. time steps = 10000 N Output parameters cross-sectional area = 0.7854 m2 A terminal velocity |vT| = 54 m.s-1 = 192 km.h-1 time to reach ~ 18 s vT t(vT)
radius of steel ball R = 20.0x10-3 m density of steel ball = 7800 kg.m-3 mass of table tennis ball m = 12.70x10-3 kg drag coefficient CD = 0.445 density of air F = 1.225 kg.m-3 viscosity of air F = 1.789x10-5 Pa.s max time tMax = 3.00 s No. time steps N = 10000 Output parameters table tennis ball steel ball free fall Fdrag = 0 terminal velocity vT [m.s-1] 8.79 86 t = 3.00 s a [m.s-2] 0.049 8.75 9.80 t = 3.00 s x [m] 20.9 43.3 44.1 t = 3.00 s v [m.s-1] 8.77 28.3 29.4 t = 3.00 s Reynolds number NR 7.8x104 It is “true” that heavier objects do fall faster than lighter ones. table tennis ball steel ball Example A falling skydiver mscript mec_drag.m We can model a falling skydiver falling from rest using the numerical approach where the resistive force or drag force is Input parameters radius (estimate) R = 0.500 m mass m = 70 kg mass entered and not calculated from density drag coefficient CD = 0.5 density of air F = 1.225 kg.m-3 viscosity of air F = 1.789x10-5 Pa.s max time tMax = 20.00 s No. time steps N = 10000 Output parameters cross-sectional area A = 0.7854 m2 terminal velocity |vT| = 54 m.s-1 = 192 km.h-1 time to reach vT t(vT) ~ 18 s