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# Gravitational Potential Energy Formula

We all pretty well know about the potential energy but gravitational potential energy is something that is easy to understand when you understand the potential energy. Besides, in this topic, you will study the gravitational potential energy, Gravitational potential energy formula, derivation of the formula, and solved example. ## Gravitational Potential Energy

Some energies are easier to understand and imagine while some are hard to explain or understand. Furthermore, kinetic energy can be easily understood because in this, the movement of the object is slow or fast. But, potential energy is difficult to explain because there is no movement in potential energy.

Besides, according to physics, energy is something that can neither be created nor destroyed but it changes form from one to another and this is the concept of conservation of energy. Also, when a car moves uphill and slows to a stop because of how steep it is, then where does this energy go? Moreover, what happens when you lift a box from the ground in your arms using your muscular energy then where does that energy go?

The answer to both of these is that they turned into gravitational potential energy (GPE). Furthermore, this energy is the like the height energy means that the higher you lift an object the more GPE it will have.

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### Why Gravitational Potential Energy must exist

So, how do we know that things have energy just for the reason that they have height? Let’s think about it.

First of all, lift a ball high above your head and from there drops it. Furthermore, during the fall you will see that it moves fast right up until it hits the ground. Moreover, it proves that energy can neither be created nor destroyed but can be moved from one form to another form. Also, it proves that whatever energy we put has to go somewhere.

#### Step 1

First of all, you use your muscle strength to lift the ball and by doing so you do work. Also, this energy came from the food you eat, that originally comes from the sun throughout the food chain. Moreover, when you lift the ball you use energy and since it has to go somewhere. So, we conclude that it is stored inside the ball in the form of gravitational potential energy.

#### Step 2

When you release the ball it falls, this means that energy really is stored inside the ball and after releasing it, it starts to move. Moreover, during its fall the ball gains kinetic energy and gets faster all the time. In this way gravitational potential changes into kinetic energy.

#### Step 3

At this point, the ball is almost touching the ground and has almost reached the point from where you have picked up the ball. Furthermore, at this point, the ball has its maximum speed an also the kinetic energy. Moreover, at this point, the kinetic energy is equal to gravitational potential energy it had before you dropped it.

In addition, when the ball hit the ground its energy is absorbed by the earth in two ways: first in the form of heat that dissipates in the ground and second in the form of movement of earth itself.

### Gravitational Potential Energy Formula

The gravitational potential energy formula is equal to the mass times the force of gravity where g is a constant valued 9.8 $$m/s^{2}$$ times the height of the object.

Potential energy = mass × gravity × height

$$E_{grav}$$ = PE = mgh

### Derivation of the Gravitational Potential Energy Formula

m = refers to the mass of the object in kilogram (kg)
g = refers to the constant gravity that is 9.8 $$m/s^{2}$$
h = is the height of the object in meters (m)
PE = refers to the potential energy in joules (J) or $$kg \cdot m^{2}/s^{2}$$

### Solved Example

#### Example 1

Suppose a basketball has a mass of 2.2 kg and it falls off a window ledge to the ground 50 m beneath. So, calculate the gravitational potential energy of the ball when it arrives beneath?

Solution:

mass = 2.2 kg
height = 50 m
gravity = 9.8 $$m/s^{2}$$

Putting values in the formula

$$E_{grav}$$ = mgh
$$E_{grav}$$ = (2.2 kg) (9.8 $$m/s^{2}$$) (50 m)
$$E_{grav}$$ = 1078 $$kg \cdot m^{2}/s^{2}$$ = 1078 J

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