Gravitational potential energy

Introduction 

Gravitational potential energy is associated with the gravitational field of a planet or a celestial body which affects the mass of an object held at a vertical distance from the surface of the celestial object or the planet.

There is a direct correlation between the mass of the object and the gravitational potential energy of that particular object. For instance, objects with a more excellent mass value would possess more gravitational potential energy and vice-versa.

It is important to note that the energy acquired by an object as it falls from a specific height towards the earth’s surface is both potential energy and kinetic energy. Up to a certain distance, before the object touches the ground level, the potential energy acts on it.

And before reaching the ground level, the energy acquired by the object turns into kinetic energy.

The equation for gravitational potential energy is thus expressed as follows:

Gravitational= m x g x h

Where,

m denotes the mass of the object (in kgs)

g denotes the gravitational pull of the earth (9.8 N/kg on the surface of the earth)

h denotes the height of the object from the surface of the earth (in metres)

Gravitational potential energy formula

The gravitational potential energy is the energy acquired by an object due to its gravitational pull based on its vertical position on the earth’s surface. This energy is mainly dependent on two primary factors apart from the gravitational pull of the earth, i.e. the mass of the object and the vertical height of the object from the surface of the earth.

To explain the gravitational potential energy in simple terms, we must first understand that any object held by an external force above the earth’s surface is being influenced by the earth’s gravitational pull.

We can take the example of two marble balls:

• Place a marble ball on the surface of a table and hold another above the surface level of the table.
• The marble ball, which is being held above the surface level of the table, would undoubtedly pose more gravitational potential energy than the marble ball placed on the table.

The gravitational potential energy is most effectively used for calculating the gravitational force acting on an object which is closer to the surface of the earth. And, the gravitational acceleration is always assumed to be 9.8 m/s2

Now, since the force required to lift an object from the earth’s surface is equal to the object’s weight, it directly relates to the fact that the gravitational potential energy is equal to the weight of the object multiplied by the height to which it is being lifted.

The formula for gravitational potential energy is expressed as follows:

Gravitational = weight x height = mgh

Where, the gravitational acceleration is assumed to be at a constant, i.e. 9.8 m/s2

Gravitational energy

Gravitational energy can be defined as the energy stored in an object due to its position on the earth’s surface. And, as the term suggests, this energy is affected by the earth’s gravitational pull.

According to this analogy, the closer the object is to the earth’s surface, the lower the gravitational energy of the object would be and vice-versa. The gravitational energy, in other terms, is also known as the gravitational potential energy.

It is the earth’s gravitational field that makes the objects on the surface of the earth fall towards each other. And, it is essential to note that the gravitational potential energy increases as two objects are brought further apart.

The equation for the gravitational potential energy acting between two objects interacting with each other can be expressed as follows:

U = -GMm/R

Where,

M and m denotes the masses of the two objects

R denotes the distance between the two objects

And, G denotes the gravitational constant and it is equal to 6.67 x 10-11 Nm2/kg2

When the objects are closer to the surface of the earth, the gravitational field acting on the objects becomes constant, and the gravitational potential energy reduces to:

U = mgh 

where m denotes the mass of the object.

g denotes the gravitational pull of the earth (9.8 N/kg on the surface of the earth)

h denotes the height of the object from the surface of the earth (in m)

Example 1: An object of mass 50 kg is placed at the top of a hill. Height of the hill is 250 m from the sea level. What is the gravitational potential energy of this object?

Ans: Here given parameter are following

M = 50 kg

h = 250 m

We know that, gravitational potential energy can be find out by following formula

U = Mgh

g = acceleration due to gravity = 9.8 m/s2

So gravitational potential energy

U = 50kg x 9.8 m/s2 x 250m

U = 122500 J = 122.5 kJ

Example 2: What is the gravitational potential energy of the moon with respect to earth? Consider the distance between moon and earth is 384,400km, mass of earth 5.98 x 1024 kg and mass of moon is 7.35 x 1022 kg.

Ans: Given data

 Mass of the earth Me =  5.98 x 1024 kg

Mass of the moon Mm = 7.35 x 1022 kg

Distance between the earth and the moon R = 384,400 km= 384,400,000 m

Gravitational potential energy can be calculated by following formula

U = GMeMm/R

Here G is gravitational constant and it is equal to 6.67 x 10-11 Nm2/kg2

By substituting all values in formula we will get U = 7.63 x 1022 Megajoule.

 Gravitational potential

Gravitational potential at a point is the amount of work done in bringing a body of unit mass from infinity to that point. The gravitational potential is expressed as follows:

V = -GMR

Hence, the gravitational potential can be defined as the work done to bring an object from infinity to a certain point which is the point of the gravitational potential of that object. The gravitational potential is thus expressed as the ratio of work done per unit mass.

Since the SI unit of work is – joule and the SI unit of mass is kilograms, the unit of measurement of gravitational potential becomes   Jkg-1.

Conclusion

Gravitational potential energy can be defined as the energy an object possesses in terms of its vertical position on the earth’s surface and the object’s mass. The energy acquired by the object due to the gravitational energy is influenced by the earth’s gravitational field and the distance of the object from the earth’s surface.

The gravitational potential energy is also known as the gravitational energy, and the following expression expresses it:

U = mgh