Newton’s law of universal gravitation – problems and solutions

1. The distance between a 40-kg person and a 30-kg person is 2 m. What is the magnitude of the gravitational force each exerts on the other. Universal constant = 6.67 x 10-11 N m2 / kg2

Known :

m1 = 40 kg, m2 = 30 kg, r = 2 m, G = 6.67 x 10-11 N m2 / kg2

Wanted : the magnitude of gravitational force (F) ?

Solution :

Newton's law of universal gravitation – problems and solutions 1

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2. The distance between Earth and Moon (r) is 3.84 x 108 m. What is the magnitude of gravitational force each exerts on the other?

Known :

Earth’s mass (mE) = 5.97 x 1024 kg

Moon’s mass (mM) = 7.35 x 1022 kg

The distance between Earth’s center and the Moon’s center

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(r) = 3.84 x 10
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8 m

Universal constant (G) = 6.67 x 10-11 N m2 / kg2

Wanted: The magnitude of gravitational force (F)

Solution :

Newton's law of universal gravitation – problems and solutions 2

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3. What is the distance from the Earth, the magnitude of the gravitational force of the earth and the moon is zero?

Known :

Earth’s mass = 5.97 x 1024 kg

Moon’s mass = 7.35 x 1022 kg

The distance between Earth’s center and Moon’s center

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(r) = 3.84 x 108 m.

Universal constant (G) = 6.67 x 10-11 N m2 / kg2

Wanted: distance from Earth

Solution :

Newton's law of universal gravitation – problems and solutions 3

Net gravitational force is zero.

Newton's law of universal gravitation – problems and solutions 4

Use quadratic formula :

A = – 6.35

B = – 7.68 x 108

C = 87.76 x 10-14

Newton's law of universal gravitation – problems and solutions 5

 

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