There is the story. It claims the boy was hit by a meteorite traveling at 38 000 mph. We can easily get the kinetic energy by estimating its mass. But here is my question:
Based upon the reasonable estimations we can make about the situation (air density, mass of object, etc), how could we calculate how hot the object was when it allegedly hit him? Or grazed him (I figure it would have had to graze him not to rip his hand off or worse).
My initial plan was to integrate the force of drag equation from a distance 0 to the top of the atmosphere, and just assume that all friction went to heat energy. Any thoughts on that method?
By the way I am referring to the equation f = -(1/2)CpAv^2
So you'd have
W = -(1/2)CpA ∫ (dx/dt)^2 dx
from the ground to the top of the atmosphere, right?
a.) would that even work?
b.) is my math close or have I lost a concept or something somewhere?- that is, is this a method you could use to determine energy from friction using the drag force equation?
If so, could we fudge a bit and let v be a constant? Then couldn't we pull this number?
W = -(1/2)CpA ∫ (dx/dt)^2 dx
= -(1/2)CpA ∫ (v^2) dx
= -(1/2)CpA(v^2) ∫ dx
=
= -(1/2)CpA ( 38 000 mph^2) *distance from top of atmosphere to earth
Safe to say that appears to be fairly easy. But is it a reasonable assumption that the magnitude of the velocity of the falling meteorite didn't change all that much due to earth's gravity? I assume if its moving really fast maybe? If not I guess we could just integrate with v as a variable, but that seems like a bit of a math headache.
Hmmm... lets say the object's final velocity is v. If we assume its initial velocity (at entry into the atmosphere) is somewhat close to its final velocity, say, v - ∆v , what would t be? So, let ∆v = 3000 m/s.
v = v - ∆v + at
∆v/a = t
(3000 m/s)/(9.8 m/s^2) = t
t = about 5.1 minutes. If that is reasonably close to how long it takes a meteorite to fall, then I say assuming v is constant is reasonable. Then again... maybe not. Especially since the meteorite will certainly lose a bunch of mass as it falls, making m a variable, which in turn makes the force due to friction a variable, since the object's cross sectional will change with time, and of course air density is also a variable with respect to distance, which naturally makes all of this a waste of time...
Okay I quit this one for now. Enjoy.
