Solved Examples on Potential Energy

Example 1: Find the potential energy of an object of mass 10 kg when it is raised at a height of 6 m above the ground. Take, g = 10 m s^–2.

Solution:

Given

Mass of the object m = 10 Kg

Height above the ground h = 6 m

Potential energy E_p = ?

We Know that

E_p = mgh

E_p = 10 × 10 × 6

E_p = 600 J

The Potential Energy of the object is 600 J

Example 2: A Ball of mass 22 kg is at a certain height above the ground. If the potential energy of the object is 880 J, find the height at which the object is with respect to the ground. Take, g = 10 m s^–2.

Solution:

Given,

Mass of the Ball, m = 22 kg

Potential energy, E_p = 880 J

Height above the ground h = ?

We Know that

E_p = mgh

880 = 22 × 10 × h

h = 880/220

h = 4 m.

The height of the object is 4 m.

Example 3: An asteroid is coming toward the earth. Its height above the ground is 1000 km. Its estimated potential energy is almost 4× 10¹⁵ J. Find out the mass of the asteroid.

Solution:

Given,

Potential energy E_p = 3.72 × 10¹³ J

Height of the asteroid, h = 1000Km = 10⁶ m

Mass of the asteroid, m =?

We know that

E_p = mgh

3.72 × 10¹³ = m × 10 × 10⁶

m = 3.72 × 10⁶ Kg

Mass of asteroid is 3.72 × 10⁶ Kg

Example 4: A spring has a strength length of 0.7 m. Take k= 16. What is it’s elastic potential energy?

Solution:

Given

k = 7

Length = 0.7 m

Elastic Potential Energy = ?

U = ½ kx²

U = ½ × 16× 0.7× 0.7

U = 3.92 J

Example 5: A spring with spring force constant k= 12 has an elastic potential energy of 24 J. Find out the change in the length of the spring in m.

Solution:

Given,

k = 12

U = 24 J

Length in m = ?

U = ½ kx²

24 = ½ ×12 × x²

x = 2 m

Thus, the change in the length of the spring is 2 m.

Potential energy in physics is the energy that an object possesses as a result of its position. The term Potential Energy was first introduced by a well-known physicist William Rankine, in the 19th century.

Gravitational Potential Energy, the elastic potential energy of an elastic spring, and the electric potential energy of an electric charge present in an electric field are all commonly used types of potential energy. In general, the work done by the force on an object for making it acquire a specific position is stored as the potential energy of that object.

For example, if we take an electric charge at infinity and bring it into the electric field of any other electric charge then the work done here is stored as the electric potential energy of that charge.

Let’s understand more about potential energy definition, formula, examples, types, and others in this article.