Sean Carroll on Cosmology and Particle Physics Lecture 2 of 5

[sbergman27]

23:45 Ouch! Presumably not all of them made it to escape velocity. What's terminal velocity for a ball bearing falling through Earth's atmosphere?

[iasedu]

@sbergman27 sqrt((2mg/pACd)) where p is the density of the air and Cd is the drag coefficient. If I remember it correctly, shouldn't be too hard to get some results. (If you are curious enough!)

[sbergman27]

@iasedu Thanks for the reply. :-)

For a 0.5 cm radius ball bearing, that works out to 95 m/s (about 210 mph) assuming that it sheds excess velocity and hits with the Vₜ indicated for the lower atmosphere. Like I say: "Ouch!"

r = 0.5 cm

m = 4.2 g

g = 980 cm/s²

ρ = 0.0012 g/cm³

Cd = 0.1

A = 0.7554

-Steve