Gravitational Potential Difference

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he gravitational interaction is the weakest interaction and it is responsible for

Holding the earth together and retaining on it the atmosphere as it is present with its life giving constituent oxygen.
Binding the earth and the other planets to that perennial source of energy which is named as the sun into a well knit solar system.
Binding the stars together into what are called galaxies.

Cause of Gravitational potential difference and interaction

Gravitational interactions include the familiar force of our weight which results from the gravitational attraction of the earth acting on us. The gravitational interactions are due to the gravitational forces which always act along the line joining the two particles and they form an action reaction pair. Even when the masses of the two particles are different the two interaction forces have equal magnitude. The attractive force that our body exerts on the earth has the same magnitude as the force that the earth exerts on us. The gravitational interaction also possess a kind of field with it called the gravitational field and this field at a ...
... point is quite often referred to simply as the field at the point and may also be defined as the space rate of change of the gravitational potential. Thus next we are going to discuss the gravitational potential shown in the fig.1.

Deriving Gravitational Potential Difference of a body

The gravitational potential difference or simply the gravitational potential V at a point r from a body of mass m is equal to the amount of work done in moving a unit mass from infinity to that point. The gravitational force and gravitational potential are zero at infinity. Thus,

V = - `int_oo^r`E dr = - `int_oo^r` (m / r2) G = - (m / r) G

Clearly this is also the potential energy of the unit mass at the point distant r from the body of mass m. so that the gravitational potential at a point is equal to the potential energy of the unit mass at that point.

Image of gravitational potential energy

Fig.1 Gravitational Potential

Conclusion for Gravitational potential difference

From the discussion, we see that the gravitational potential and the potential energy are always negative in sign and their highest value is zero at infinity. We have also seen its importance in many natural phenomena.

An object has energy when it is moving, but it can also have potential energy, which is the energy associated with the object's position.

Potential Energy, Example: a heavy brick lifted up has potential energy due to its position in relation to the ground. It can do work because when dropped it will fall because of the gravity force, allowing it to make a work output over another object receiving the impact.

A compressed spring has potential energy. For instance, the spring of a mechanical clock transforms its energy doing work to move the seconds, minutes and hour pointers.

Check this Formula of Work awesome i recently used to see.

There are several kinds of potential energy: gravitational, elastic, electric, etc.

Gravitational Potential Energy:

The gravitational potential energy is a very common example of potential energy.

The Gravitational Potential Energy (GPE) of an object of mass m at a height y over a reference level is defined as:

EPG = mgy
g is the gravity acceleration

This definition is fully compatible with the definition of work since the work needed lo lift the mass m from the reference level to the height y is Fy = Weight·y = mgy. The object has gained an energy mgy.

If we let this object of mass m to fall freely by gravity on a stake on the ground, the work on the stake will be equal to the kinetic energy acquired while falling.

This kinetic energy can be calculated by the kinematics equation vf2 = vi2 + 2gy. Since vi = 0, then
vf2 = 2gy. The kinetic energy just before striking the stake is ½mvf2. Replacing vf2 with 2gy we get ½ m·2gy = mgy.

Then, to raise an object of mass m to a height y we need a work amount equal to mgy, and once at this height y, the object has the capability of doing work equal to mgy.

Let's notice GPE depends on the object's vertical height over some reference level; in this example, the ground.

The work needed to lift an object does not depend on the lifting path. That direction can be vertical, inclined, or another, and the work to rise the object will be equal.

Also, the work the object is able to do when falling does not depend on its path.

From what level must the height y be measured? What matters here is the potential energy change and we choose a reference level convenient to solve a given problem. Once we choose it, we must keep it during the calculations.

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