   Chapter 2.7, Problem 20E

Chapter
Section
Textbook 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 = G m M r 2 where G is the gravitational constant and r is the distance between the bodies.(a) Find dF/dr and explain its meaning. What does the minus sign indicate?(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2 N/ km whenr = 20, 000 km. How fast does this force change when r = 10, 000 km?

To determine

Part (a)

To find:

dFdr

and its meaning.

Explanation

1) Formula:

Quotient rule:

f'uv=vu'-uv'v2

2) Given:

F=GmMr2

3) Calculation:

ddrF=ddrGmMr2

dFdr=r2ddrGmM-G

To determine

Part (b)

To find: force change when r=10,000

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