# 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 m^{2} / kg^{2}

__Known :__

m_{1} = 40 kg, m_{2} = 30 kg, r = 2 m, G = 6.67 x 10^{-11} N m^{2} / kg^{2}

__Wanted :__ the magnitude of gravitational force (F) ?

__Solution :__

2. The distance between Earth and Moon (r) is 3.84 x 10^{8} m. What is the magnitude of gravitational force each exerts on the other?

__Known :__

Earth’s mass (m_{E}) = 5.97 x 10^{24} kg

Moon’s mass (m_{M}) = 7.35 x 10^{22} kg

The distance between Earth’s center and the Moon’s center (r) = 3.84 x 10^{8} m

Universal constant (G) = 6.67 x 10^{-11} N m^{2} / kg^{2}

__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 10^{24} kg

Moon’s mass = 7.35 x 10^{22} kg

The distance between Earth’s center and Moon’s center (r) = 3.84 x 10^{8} m.

Universal constant (G) = 6.67 x 10^{-11} N m^{2} / kg^{2}

__Wanted:__ distance from Earth

__Solution :__

Net gravitational force is zero.

Use quadratic formula :

A = – 6.35

B = – 7.68 x 10^{8}

C = 87.76 x 10^{-14}

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