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 :

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 (m_E) = 5.97 x 10²⁴ kg

Moon’s mass (m_M) = 7.35 x 10²² kg

The distance between Earth’s center and the Moon’s center (r) = 3.84 x 10⁸ m

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

Wanted: The magnitude of gravitational force (F)

Solution :

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 (r) = 3.84 x 10⁸ m.

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

Wanted: distance from Earth

Solution :

Net gravitational force is zero.

Use quadratic formula :

A = – 6.35

B = – 7.68 x 10⁸

C = 87.76 x 10^-14

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