   Chapter 3.7, Problem 20E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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 when r = 20,000 km. How fast does this force change when r = 10,000 km?

To determine

To find: The value of dFdr and explain its meaning. What does the minus sign indicate?

Explanation

Given:

The equation for magnitude F is as given below.

F=GmMr2

Rewrite the equation as below.

F=(GmM)r2 (1)

Calculation:

Calculate the value of rate of change of force dFdr as below.

Differentiate the equation (1) as below.

dFdr=2(GmM)r3dFdr=

(b)

To determine

To find: How fast does the force change when the distance between the bodies r is 10,000km.

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