gravitational potential energy

Gravitational Potential Energy

Gravitational potential energy is an important concept, This energy is invisible you can not see, so most of the time students confused, But in this topic you will learn some new hidden concept about gravitational potential energy, I ensure you after learning this post your all doubt and concept will be clear, Each and every concept about gravitation potential energy will discuss, What is gravitational potential energy ? How gravitation potential energy is calculate and what is it real meaning ? Why gravitational potential energy value is negative What is potential energy at infinity ? So lets start.

What is gravitational potential energy ? 

Actually gravitational potential energy is not define directly any meaning, it define in terms of change in potential energy, so for change in potential energy calculation, you need to do some work.

Hence gravitational potential energy is define as work done bringing a mass from infinity to a certain point in gravitational field. This gravitational field is created by another source mass. If you don't know about potential.

Refer my previous post about gravitational potential concept

See gravitation potential energy is not for a single body or mass, It is always for a system means between two or more masses gravitational potential energy is stored in the system of masses .If you will ask what is gravitational potential energy for a single mass ? 

Well for a single mass gravitational potential energy is always zero. Wait you will see how it is zero ? As i have mentioned that potential energy is work done then who does this work ? Well external agent like you or gravitational force both does this work but when work is done by external agent then work value is positive and when work is done by gravitation force its value is negative.

Mathematical expression change in potential energy (∆U) = (-work done by internal conservative force) or Uf - Ui  = ∆U=  (-work done internal conservative force).

Now what is conservative force ? conservative force is that force in which wok done depend upon initial and final position it does not depend upon the path, like gravitational force, spring force are example of conservative force.

So Conservative forces only posses potential energy, non-conservative force like friction does not posses potential energy.

you must remember during the work done velocity must remain constant hence kinetic energy must not change.

Concept of gravitational potential energy 

Potential energy at infinity (∞) for any types of mass system or any mass configuration is assumed universally zero by scientist. Hence you use the above formula, Uf - Ui  = ∆U=  (-work done internal conservative force)

So Uf - U∞   = (-work done by gravitational force bringing each mass from infinity) so

Uf -0 = (-work done by gravitational force bringing each mass from infinity)

Uf  = (-work done by gravitational force bringing each mass from infinity) important again i am telling potential energy is not for mass, it is for design or configuration which is bringing from infinity to a certain point. see below picture.

                                                           

Gravitational potential energy

                                                                         

gravitational potential energy

Gravitational potential energy

Gravitational potential is very important concept because the same concept is used in electric potential, So potential is a general concept, Which you need to understand the concept behind potential. Whenever you see gravitational potential then you must remember, the existence of gravitational potential is due to mass.

If mass is not present then gravitational potential will not exist, Can you think why ? well if there is no mass then there is no gravitational field and if no gravitational field then there is no gravitational potential.

So you can think potential depends upon field, which may be gravitational field or electric field or magnetic field in general but here you will learn about gravitational field potential.

If you have not studies gravitational field then i will suggest you first to learn about gravitational field in my previous post so that you can better understand gravitational potential concept, You can refer link Gravitational field.

When you see electric potential this is due to charge, but the potential concept for both the cases is same. Hence you will learn in this topic, what is potential ? and how it is calculated, why need to learn potential ? and then potential energy.   

What is gravitational potential ? 

Potential word itself has not got any defined meaning, whereas potential difference is defined as "the difference in potential between two points that represents the work involved or the energy released in the transfer of unit quantity of mass from one location to the other location". So it is clear that potential is a characteristics of location or point.

Suppose there are two points A and B and a small mass m is kept at point B, now this small mass m bringing from point B to A, now you need to do some amount of work that amount of work is called potential difference between B to A.

                                                                                                                                  ←m

Mathematically written as  Va - Vb  = (Work done B to A)/m             A         W            B  

with no change in kinetic energy, means when you are bringing mass m from point B to A the speed of mass does not change during the journey from B to A.then only this formula is valid.

Potential at a point 

As i have stated potential itself is not a defined meaning in Physics, So we have taken a reference point, such that the potential of reference point will be zero. Now you can compare any new point potential from that reference point, like how much is potential at new point.   

Hence reference point was take at infinity (∞) so potential at infinity is zero, now you are able the compare any new point potential respect to infinity potential. But remember point does not have energy but whenever you bring a mass near to that point then energy is stored in mass.

So it is clear that energy is available in mass but potential at point or at location indicate how much energy will be available at that location in the body or mass, which is bring to that point. You must remember every point has some potential, If you bring a mass then energy is stored in mass, If you don't bring the mass then energy is not stored, but potential is always there.

You generally listen the peoples use potential word like, there is potential in this business, what do you understand by using this word ? Well that person is indicating about money in that business, Hence money is form of energy in Physics.
So potential indicate about energy of at point or location but when you bring a mass.         

Now from the above two point, which you have taken A and B put point B at infinity that is B(∞), now put a small mass m at infinity and bring this mass to point A, the work done will give you the potential at point A.

Now you can write mathematically  VA - V∞  = (Work done infinity to A)/m  put V∞ = 0 then you will get  VA  =  (Work done W infinity to A)/m .

what is VA ?  this is potential at point A.

Actually potential at a point does not exist, we are just comparing from infinity point potential so you are able to define potential at point A.

Hence potential at a point is define as work done per unit mass bringing  from infinity to that point A, such that without changing the kinetic energy of mass m means mass moving very very slowly from infinity to point A.

Now i hope your concept about potential and potential difference is clear.

Gravitational potential due to a mass M

                                                                 

Gravitational potential