A table-tennis ball of mass

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Simulating classical dynamical systems

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

Problem

A table-tennis ball of mass m=2.7×10−3 kgm = 2.7\times10^{-3}\,\mathrm{kg}, with drag constant b=3.8×10−4 kg m−1b = 3.8\times10^{-4}\,\mathrm{kg\,m^{-1}}, is released from rest 20 m20\,\mathrm{m} above the floor. It obeys mv˙=−mg+bv2m\dot v = -mg + bv^2 (downward negative). ((a)) Type in and run the function fall\texttt{fall} of Worked example 1.1 with Δt=0.1 s\Delta t = 0.1\,\mathrm{s} and tend=10.0 st_{\rm end} = 10.0\,\mathrm{s}. Give the number of passes it runs and the last two rows (t,y,v)(t, y, v) of the records it returns. ((b)) Turn the last step's bracket into a single landing time by dividing the overshoot by the speed in the last row, as in Section 1.7. Repeat at Δt=0.05 s\Delta t = 0.05\,\mathrm{s} and 0.025 s0.025\,\mathrm{s}, and give the three landing times, to four decimal places, and the two differences between them. ((c)) Call fall\texttt{fall} again at Δt=0.1 s\Delta t = 0.1\,\mathrm{s} with tend=1.5 st_{\rm end} = 1.5\,\mathrm{s}. Say how the returned records alone show that the ball has not landed.

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