BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.7, Problem 113E
To determine

The distances for which the gravitational force exerted by the earth on the object is between 0.0004 N and 0.01 N.

Expert Solution

Answer to Problem 113E

The distances for which the gravitational force exerted by the earth on the object is between 0.0004 N and 0.01 N are between 20,000kmand 100,000km_.

Explanation of Solution

Given:

The gravitational force F exerted by the earth on the object having a mass of 100 kg is given by F=4000,000d2 where F is the gravitational force in Newtons (N) and d is the distance between the earth and the object in meters (km).

Calculation:

To obtain the distances for which the gravitational force exerted by the earth on the object is between 0.0004 N and 0.01 N, substitute these values for F in F=4000,000d2 and solve for d.

Substitute the value F=0.0004N in F=4000,000d2 and obtain the value of d.

0.0004=4000,000d2d2=4000,0000.0004d2=10000000000d=10000000000d=100000

Now, substitute the value F=0.01N in F=4000,000d2 and obtain the value of d.

0.01=4000,000d2d2=4000,0000.01d2=400000000d=400000000d=20000

Thus, the distances for which the gravitational force exerted by the earth on the object is between 0.0004 N and 0.01 N are between 20,000kmand 100,000km_.

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