A ball is thrown straight upward from ground level with (here is taken positive upward)

PHYSICS · Multi-part · 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 upward from ground level with

v_0 = 20\,\mathrm{m\,s^{-1}}

(here

v

is taken positive upward), mass

m = 0.060\,\mathrm{kg}

, and quadratic drag

b = 0.00090\,\mathrm{kg\,m^{-1}}

that opposes whichever way it is moving. Someone writes the following, intending the loop to stop when the ball comes back down through the ground (

y < 0

) or after a generous safety time

t_{\rm max} = 200\,\mathrm{s}

: (line 1) t, y, v = 0.0, 0.0, v0 (line 2) for n in range(round(t_max/dt)): (line 3) a = -(b/m)*v*abs(v) (line 4) v_new = v + a*dt (line 5) y = y + v*dt (line 6) v = v_new (line 7) t = t + dt (line 8) if y < 0.0: (line 9) break. Run with

\Delta t = 0.2\,\mathrm{s}

, the first rows of

(t, y, v)

are

(0,\ 0,\ 20.00)

(0.2,\ 4.00,\ 18.80)

(0.4,\ 7.76,\ 17.74)

(0.6,\ 11.31,\ 16.80)

in seconds, metres and

\mathrm{m\,s^{-1}}

; the run continues with

v

falling more and more slowly and

y

still climbing, and it is only cut off by the safety cap at

t = 200\,\mathrm{s}

, with

y

still positive and rising. ((a)) Identify the line that is missing a piece of physics, and say what it should read. ((b)) Explain, from the table, why the loop never reaches

y < 0

before the safety cap intervenes.

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