Examples of Gravitational Force

Example 1: Find the gravitational force of attraction between two elephants, one of mass 1000 kg and the other of mass 800 kg, if the distance between them is 5 m.

Solution:

Given: m₁ = 1000 kg, m₂ = 800 kg, r = 5 m

The formula for gravitational force is given as: F_g = 

Here, G =  6.67 ×10⁻¹¹N⋅ m²/kg²

Substituting the values in the formula, we have:

F_g = 

F_g = 2.1 × 10^-6 N

Example 2: Find the gravitational force of attraction between a man of mass of 50 kg and a bus of mass 1500 kg, if the distance between them is 10 m.

Solution:

Given: m₁ = 50 kg, m₂ = 1500 kg, r = 10 m

The formula for gravitational force is given as: F_g = 

Here, G =  6.67 ×10⁻¹¹N⋅ m²/kg²

Substituting the values in the formula, we have:

F_g = 

F_g = 5.0025 × 10^-8 N

Example 3: Suppose the gravitational force between two bodies at a certain distance is 4 N. Find the force of attraction if the distance between them is doubled.

Solution:

Newton’s law of gravitation states that the gravitational force between two point like objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F_g = 

Equation shows that ,for given masses, if r is replaced by 2r, the force becomes 1/4th original force. Therefore ,force of attraction will become 4/4 =1 N.

Example 4: The mass of the Earth is 6 × 10²⁴ kg. The distance between the Earth and the Sun is 1.5 × 10¹¹m. If the gravitational force between the two is 3.5 × 10²²N, what is the mass of the Sun?

Solution:

Given: m_e = 6 × 10²⁴ kg, r = 1.5 × 10¹¹ m and F = 3.5 × 10²² N

Formula for gravitational force is given as: F_g = .

⇒ 3.5 × 10²² N = 

⇒ Mass of sun = 

= 1.967 × 10³⁰ kg

Newton’s Law of Universal Gravitation is used to explain gravitational force. Gravitational Force is a type of Non-contact force, the gravitational force is a force in nature that is always attractive and conservative. Gravitational Force is defined as the force of attraction experienced by two or more objects in contact. Gravitational force is determined by the formula obtained from Newton’s Universal Law of Attraction, known as the Gravitational Force Formula. Our environment is surrounded by gravity. It determines how much we weigh and how far a basketball will bounce before hitting the ground when it is thrown. The force the Earth applies to you is equal to the gravitational force on Earth. The gravitational force is equal to your weight while you are at rest on or near the Earth’s surface. Also, the presence of a gravitational field is required in the heat transfer through natural convection.