Gravitational Force between Two Light Objects

 

Gravitational force between massive objects

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Let us now calculate the force of attraction between an object of mass 50 kg and Earth. The mass of the Earth is about 6x10²⁴kg. The distance between the Earth and the object is approximately 64x10⁵m. The force of attraction between the object and the Earth

This force is so strong that we cannot ignore it.

Now let us calculate the force of attraction between Earth and the Sun.

The mass of the Earth = 6x10²⁴ kg

The mass of the Sun = 1.99x10³⁰ kg

The distance between the Earth and the Sun = 15x10¹⁰m

This force is very large and it is this force which keeps the planets in their respective orbits.

From the above examples, it is very clear that the gravitational force between two objects of ordinary size is very small, whereas the force is very large when atleast one of the objects is massive.

Problems

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1. Calculate the force of attraction between Earth and the Sun.

Solution:

Given Mass of the Sun =10³² kg

Mass of the Earth = 6x10²⁴kg

Distance between the Sun and Earth = 150x10⁹m

F

2. What is the force existing between two spheres of mass 10 kg each and placed 100 cm apart?

Solution:

m₁ = m₂ = 10 kg

Distance d =100 cm

G=6.6734 x 10^-11 Nm²/kg².

3. Calculate the force of attraction existing between the Earth and an object of mass 50kg placed on the surface of the Earth.

Solution:

Given the mass of Earth =6x10²⁴ kg

Radius of Earth = 6400 km = 6400x10³ m

Mass of Earth (m₁) = 6x10²⁴ kg

Mass of object (m₂) = 50 kg

G=6.6734x10^-11 Nm²/kg²

Distance between the object and Earth = radius of the Earth = 6400000m

= 3.1281x109 N