A Study of Gravitational Potential Energy

When anything is released into open space, it tends to fall. This is a very regular occurrence in our daily lives. When everything is released into free space, it gravitates towards the Earth. The first person to recognise this was Sir Isaac Newton. He noticed an apple falling from the tree and began his investigation into its preferred downward motion. He came to the conclusion that not only does the Earth draw everything towards itself, but that everyone else in the universe does as well. This is a property that a body has as a result of its mass.

Gravitation

Gravitation is a force that claims that all objects on Earth and in space are attracted to one another. The gravitational force exerted on an object is proportional to its mass; the greater the mass of an object, the greater the gravitational force exerted on it by other objects. All visible items, such as a pen, eraser, planets, mobile phone, watch, and refrigerator, are attracted to one other in some way. With the Electromagnetic Force and the Nuclear Force, gravity is one of the non-contact forces.

Universal Law of Gravitation

Newton was motivated to discover the connection between falling bodies and celestial motions, according to early versions, when he watched an apple fall from a tree and thought that if the gravitational force could reach above the ground to a tree, it could also reach the Sun. The idea of Newton’s apple is a part of mythology all around the world, and it may or may not be true. It is held in high regard because Newton’s universal law of gravitation and laws of motion answered long-standing issues about nature and supported the idea of nature’s underlying simplicity and unity.

Scientists continue to hope that their continuous investigations into nature will reveal fundamental simplicity. The gravitational force is a straightforward force. It is always appealing, and its attractiveness is solely determined by the masses involved and the distance between them.

Newton’s universal law of gravitation states, that every particle in the world attracts every other particle along a line connected by a force. The force they exert on each other is proportional to the product of their masses and inversely proportional to their separation.

Gravitational Potential Energy

Gravitational Potential Energy is defined as a body’s energy arising from the gravitational force, or when the gravitational force works on a body and produces gravitational potential energy. The amount of work done on the body by the force is now the change in potential energy if the position changes owing to force.

Let’s suppose we have two items, one A and one B. Assume that B’s location changes only as a result of some force. Assume M’s location is shifting due to gravitational pull, with a corresponding shift in potential energy. The gravitational pull does the same amount of work as the change in the item’s location.

As a result, the gravitational force will accomplish the same amount of work as the shift in potential energy from P to Q. Assume P is in the first position and Q is in the second. The effort required to move the item from position 1 to position 2 is equal to the potential energy change, which is equal to the potential energy at point 2 minus the potential energy at point 1.

• Gravitational potential is the amount of work done per unit mass to move a body from infinity to a certain place.
• It’s represented by the letter U.
• The SI unit for gravitational potential is J/Kg.
• The gravitational force gives rise to the potential body. The work done on the body by the force is the change in potential energy if the position changes as a result of the force.

Gravitational Potential Energy Formula

Mathematically, gravitational potential energy is the product of mass(m), acceleration due to gravity(g) and height(h) above the ground and it can be given as:

U=mgh

Derivation of Gravitational Potential Energy

When a particle travels an indefinitely short distance, dr. The gravitational force’s work on the second particle is represented by -Fdr.

dW=-Fdr  ——- (1)

Here,

F is gravitational force and it is given by,

F=G×[(m1×m2)/r2]

F =  gravitational force between the two bodies

g =  gravitational constant. Its value is 6.67×10-11Nm2/kg2

m1 and m2= masses of the two bodies

r = distance between the centre of the two bodies

Putting the value of F in equation (1) we get,

dW=[G×[(m1×m2)/r2]dr

W= ∞r[G×[(m1×m2)/r2]dr

W= G×(m1×m2)∞r1/r2]dr

W= G×(m1×m2)[(1/r)-(1/∞)

W=-G×[(m1×m2)/r2]

As because work done is stored as potential energy U, gravitational potential energy at a distance ‘r’ from the source mass is calculated as follows:

U=-G×[(m1×m2)/r2]

Conclusion

Gravitational potential energy refers to the work that a body needs to do against gravity in order to arrive at a specific position. In other words, gravitational potential energy is the amount of energy that an object has or gains as a result of a change in the position of its gravitational field. An item possesses some form of energy since energy cannot be produced or destroyed, even when it is at rest (Which is converted to kinetic energy, when it starts to move). This form of energy is referred to as potential energy.