Potential Energy for Class 9

Life is impossible without energy. The demand for energy is ever increasing. Where do we get energy from? The Sun is the biggest natural source of energy to us. Many of our energy sources are derived from the Sun. We can also get energy from the nuclei of atoms, the interior of the earth, and the tides.

The word energy is very often used in our daily life, but in science we give it a definite and precise meaning.

            The object which does the work loses energy and the object on which the work is done gains energy.   

            Any object that possesses energy can do work.

            The energy possessed by an object is thus measured in terms of its capacity of doing work. The unit of energy is, therefore, the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work. Its unit is Kgm²s^-2

            Joule, unit of work or energy in the International System of Units (SI) is equal to the work done by a force of one newton acting through one metre. We may also say,

            It is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of the force’s motion through a distance of one metre.

            Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J.

Forms of Energy

            There are various forms of energy few of which are Mechanical energy (which may be Potential energy, or Kinetic energy or a mix of both), Heat energy, Chemical energy, Electrical energy and Light energy.

            Here we will discuss an important type among them, The Potential Energy.

Potential Energy

Few examples of Daily Life

             Take a rubber band. Hold it at one end and pull from the other. The band stretches. Release the band at one of the ends. What happens? The band will forcefully tend to regain its original length. From where did that force develop in the rubber band.  Obviously, the band had acquired energy in its stretched position. • How did it acquire energy when stretched?

            Take a slinky / spring.  Stretch it.  Now, leave one of the ends.  What happens?  Again it squeezes with force. Why? Where did it get the energy to come back immediately? 

            Lift an iron ball through a certain height. It begins to fall when released. Let it fall on wet sand.  It will create a depression.  Now drop the same ball from a greater height and watch the depression. We see that this depression is more than the earlier one.  What do we infer?  If raised to a greater height the ball can do more work; it means it possesses more energy. From where did it get the energy?  

            Take a toy car. Wind it using its key. Place the car on the ground. Did it move?  From where did it acquire energy? If we wind more the speed of the car and the distance travelled by it increases. It means the energy acquired depend on the number of windings?  How is it

            Make a bow. Place an arrow made of a light stick on it with one end supported by the stretched string. Now stretch the string and release the arrow. Notice the arrow flying off the bow. What makes the arrow fly forcefully.  Had you noticed the change in the shape of the bow. The energy stored in the bow due to the change of shape when we pulled it back is used in the form of kinetic energy in throwing off the arrow.

            In the above situations, the energy gets stored due to the work done on the object. The energy transferred to an object is stored as potential energy if it is not used to cause a change in the velocity or speed of the object.

            You have to apply energy for stretching the rubber band, or stretching the spring, or lifting the iron ball up above the ground, or winding the key of the toy car, or pulling the bow towards yourself.   You have to apply energy means you have to do work while doing all those activities mentioned above. The energy so transferred gets stored as potential energy.

            The potential energy possessed by the object is the energy present in it by virtue of its position or configuration.  [stress within itself, electric charge and some other factors also account for it, but the same is not required at this level.]

            [If an object gains energy due to movement, it is Kinetic Energy. Rest all types of energy may be called Potential Energy.]

            [There may be many types of Potential Energy viz. Gravitational Potential Energy, Elastic Potential Energy, Electric Potential Energy, Nuclear Potential Energy, Chemical Potential Energy, Intermolecular Potential Energy etc.]

            For class 9^th students we shall be taking up only Gravitational Potential Energy.

POTENTIAL ENERGY of an object at a height or GRAVITATIONAL POTENTIAL ENERGY

            An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy. [In fact it depends on its mass and its distance from the center of mass of another object].

            The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

Derivation of Kinetic Energy Formula

            Consider an object of mass, m. Let it be raised through a height, h from the ground.

            A force is required to do this. The minimum force required to raise the object is related to the mass of the object. 

We know that F = ma, so we may write F = mg.

            The object gains energy equal to the work done on it. Let the work done on the object against gravity be W then, the work done,

W = force × displacement = mg × h = mgh.   

            Since work done on the object is equal to mgh, an energy equal to mgh units is gained by the object. This is the potential energy (PE) of the object.

So, Potential Energy, Ep = mgh

POTENTIAL ENERGY – Points to be remembered:

• The potential energy of an object at a height depends on the ground level or the zero level you choose. An object in a given position can have a certain potential energy with respect to one level and a different value of potential energy with respect to another level.
• It is useful to note that the work done by gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along which the object is moved.

• A moving thing may have potential energy also due to its height or other reasons but if it is not moving and if it is capable of performing some work it is only and only potential energy.

          Practice Problems:

1. Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8 ms^–2.

Solution: Mass of the object, m = 10 kg, displacement (height), h = 6 m, and acceleration due to gravity, g = 9.8 ms^–2.

Potential energy = mgh = 10 kg × 9.8 ms^–2 × 6 m = 588 J.

Ans.  The potential energy is 588 J.

2.  An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground.Given, g=10ms^–2.

 Solution: Mass of the object, m = 12 kg, potential energy, Ep = 480 J.

            Ep = mgh

So,  480 J = 12 kg × 10 ms^–2 × h

Or,         h = 480 J    =4 m

                                      120 kg ms^–2  

Ans. The object is at the height of 4 m.

Please Note: Notes on kinetic energy are also available on this site. You may click below to reach there.