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September 30, 2014

September 30, 2014

Posted by **shelby** on Wednesday, March 19, 2008 at 6:34pm.

- physics -
**Damon**, Wednesday, March 19, 2008 at 8:29pmfind KE as a function of radius slice dr

from r = 10^10^3 to r = 150*10^3

208 km/hr /3.6 = 57.8 m/s

Velocity = m r + b linear

57.8 = m (10*10^3) + b

0 = m( 150*10^3) + b

so solve for slope and intercept

m = -.413 * 10^-3

b = 61.9

so

v = 61.9 - .413*10^-3 r

the volume at radius r = 2 pi r dr(5550)

so the mass at radius r = .891*5550* 2 pi r dr

so the KE at radius r = (1/2) (.891*5550* 2 pi r dr) (61.9-.413*10^-3 r)^2

when you square that and multiply by r dr you will get terms like

a r + b r^2 + c r^3

which will integrate to

a r^2/2 + b r^2/3 + c r^4/4

evaluate that integral at r = 10*10^3 and at 150*10^3 and you have it

- physics -
**FFttr**, Friday, March 21, 2008 at 8:07pmWhere did 3.6 come from?

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