A payload of mass falls from a burst weather balloon casing

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 payload of mass

m = 0.50\,\mathrm{kg}

falls from a burst weather balloon casing. As well as the usual quadratic drag, the residual gas trapped in the casing gives it a constant upward force

F_b

, independent of speed. Taking

v

negative downward, its equation of motion is

m\dot v = -mg + bv^2 + F_b.

Here

b = 0.020\,\mathrm{kg\,m^{-1}}

and

F_b = 0.90\,\mathrm{N}

. (a) Set

\dot v = 0

and derive an expression for the terminal speed

v_\infty

(its magnitude) in terms of

m

g

b

and

F_b

. (b) Evaluate

v_\infty

for the numbers above, to three significant figures. (c) Say in one sentence how this number could be used to check a program written for this modified fall.

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