SOLUTION: Need help with this calculus problem: Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is F = GmM/r2 dF/dr

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Question 915039: Need help with this calculus problem:
Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is
F = GmM/r2
dF/dr = -2GmM/r^3
(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 4 N/km when r = 30,000 km. How fast does this force change when r = 15,000 km?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 4 N/km when r = 30,000 km.
dF%2F%28dr%29+=+%28-2GmM%29%2Fr%5E3

Substitute -4 for dF%2F%28dr%29 and 30000 for r

-4+=+-2GmM%2F30000%5E3

-4%2A30000%5E3+=+-2GmM

-1.08%2A10%5E13+=+-2GmM

Substitute -1.08%2A10%5E13 for -2GmM in

dF%2F%28dr%29+=+%28-2GmM%29%2Fr%5E3

dF%2F%28dr%29+=+%28-1.08%2A10%5E13%29%2Fr%5E3

How fast does this force change when r = 15,000 km?

Just substitute 15000 for r in

dF%2F%28dr%29+=+%28-1.08%2A10%5E13%29%2Fr%5E3

dF%2F%28dr%29+=+%28-1.08%2A10%5E13%29%2F15000%5E3

dF%2F%28dr%29+=+-32N%2Fkm

Edwin