Potential Energy

What is potential energy? Potential energy and kinetic energy are the two forms of energy. Potential energy is the energy stored in a system that depends on the various parts included in the system. Or, we can say that the potential energy of an object is energy stored due to the role of the object. In the state of potential energy, the object is not doing any work, or the object is not moving. It is the tendency to do work or the inclination to move. A body that is at rest is full of energy. 

What is potential energy?

Potential energy is not considered for a single object; it is calculated as a property of a system. For example, if we consider the earth and a raised ball, the amount of potential energy is the distance between them. As the distance increases, the energy also increases. The potential energy is minimum when the ball is lying on the ground. The potential energy at infinity is zero since potential energy is directly proportional to acceleration due to gravity, and gravity at infinity is zero.

Potential energy cannot be transferred from one object to another.

Types of potential energy

Potential energy can be present in a few types:

1) Gravitational potential energy

Gravitational potential energy is the energy stored in an object due to its vertical height or position. The energy stored in an object is a result of the gravitational force of attraction of the earth acting on the object. Object’s height and weight contribute to it. As the object’s height from earth increases and as the object’s weight increases, the gravitational potential energy also increases. That is, height and weight are directly proportional to gravitational potential energy. A girl sitting at the top of a slide tends to move down, so she has potential energy. Ripe fruit before it falls and a car parked at the top of a hill are some examples of gravitational potential energy. 

2) Elastic potential energy

Elastic potential energy is energy stored in an object due to the application of a force that deforms a flexible object. The energy is stored in a stretched or compressed object. The stretch or compression is directly proportional to the amount of elastic potential energy stored. As the amount of stretching increases, the amount of elastic potential energy also increases. A compressed spring is an ideal example of this type of energy. A compressed spring and a stretched spring have this form of energy until they reach their original state.

The diving board, just before the diver’s jump, and a stretched rubber band are some examples of elastic potential energy.

3) Magnetic potential energy

Magnetic potential energy, chemical potential energy, and electrical potential energy are some of the other types of potential energy. Energy formed in bonds of chemical substances can be named as chemical potential energy. A charged battery can store chemical energy, which might change to electrical energy later.

The formula for potential energy

The potential energy is a product of the mass and height of the body and the acceleration due to gravity. The standard symbols used for potential energy are PE, U, and V. The formula for calculating potential energy is:

 U= m×g×h

or, U =mgh

Where, 

m = the mass of the body

g = acceleration due to gravity    

h = height of the body from the reference point 

Features of potential energy: 

Features of potential energy: 

• The unit of potential energy in SI (The International System of Units) is Joule (J).   
• The value of g is 9.8 m/s².     
• Gravitational potential energy has the same formula.

                        Ug=mgh

• The Elastic potential energy of a body is calculated as,

                       U = ½ k Δ x² 

 Where,

 U=elastic potential energy 

K=spring constant 

Δ x = change in position 

Examples of Potential Energy

1. A mass of 8 Kg is taken from the ground to the height of 120m. Find the potential energy of the object?

Ans.  Here,

m=8 N

G=10 m/s²

 H= 120 m

The potential energy of a body,  

U= mgh

= 8×10×120 J

= 9600 J

While solving problems, the value of g can be taken as 10 m/s²

2. Arun pulls a spring with a spring constant k=100 N/m stretching it from its rest length of 0.20 m to 0.30 m; what is the elastic potential energy stored in the spring?

Ans. The elastic potential energy of a body is:

U = ½ k Δ x²  

Here,

K= 100 N/m

 Δ x= 0.20-0.10

= 0.10 m

Therefore,

U= ½ ×100×(0.10)2 J

U = ½ ×100×0.01 J

= 0.5 J

3. A body of mass of 10Kg is taken from the ground for 10 m uphill on the wedge. The wedge makes an angle of 30° with the ground. Find the potential energy of the block?

Ans:  Here, we have to find:

Ug = mgh

This wedge is in the form of a right-angled triangle with one angle is 30°.

m is given equal to 10 N. And the given height is the length of the inclined plane, which is taken as l. 

L=10 m

Vertical height h is not given 

To find h,

We can use the formula for the right-angled triangle 

Therefore 

Sin30 = h ⁄ L              

        1 ⁄ 2 = h ⁄ L    

        L ⁄ 2 =h

        10 ⁄ 2 = h

     h= 5

Therefore,

U= mgh

   = 10×10×5 J

   = 500 J

Conclusion

Potential energy is one of the forms of energy besides kinetic energy. It is considered the energy of a system. It is the energy stored in a system that depends on the parts included in the system. It can be gravitational, electrical, magnetic, and chemical in forms. Potential energy can be calculated as the product of mass, height, and acceleration due to gravity.