Deriving The Formula For Gravitational Potential Energy

In this video I derive a very commonly used formula in physics (-GMm/r) that is often left unexplained by teachers in high school/sixth form classes. Deriving a formula for gravitational potential energy requires just some basic integration of polynomials and a solid understanding of the definition of gravitational potential energy (which is explained in great depth during the video)

[billelguechi]

this is the masterpiece that I've been looking for for a decade ♥

[michaelbengston]

Hi there, just wanted to say great video! What you have on this channel is really special, and the nice visuals really help with understanding too. Like Parv already said keep at it, it will all pay of I am sure of it :)

[elliottmarcel]

Hey, I just wanted to say thank you for making this video. Often in physics, I often feel frustrated because I feel that I don't understand equations that are given to, I don't understand the explanation behind them, how they were formed, and how the derivation leads to the equation doing what its supposed to do. This video really helped me understand ths work of gravity euation/ concept, and I now feel my frustration has been relieved. You earned a new subscriber

[parvbadhera]

hey buddy. i just wanna say. dont ever think to stop. because believe me your videos are great. you will succeed

[adamraiyan]

Bro. You have the greatest visualization vid. Dont stop !

[parvbadhera]

also can i say that -gMm/r is also the work done to put that mass from that point to ground. And that means that the energy spent to take the object from infinity to that point would be equal to the energy from that point to earth under only earths gravitational field.

[alex-c]

Very helpful and well explained video bro thank you. And great visual effects to show the physics concepts!

[danishheikal]

hi just want to ask... why the graph in 2:58 shows infinity is the upper limit while r is the lower but in 3:04, u put the upper limit as r while the lower limit is infinity?

[TheRandomQubeofficial]

This video was amazing and you explained it very well! Keep making such awesome videos.

[linusbao]

I understand the math behind the derivation, I just don't understand why conceptually PE is defined as the work done by some external force in bringing 2 bodies from infinitely far away to the distance they are now. Why is potential energy defined this way? Also, is this a definition that can be used to derive other forms of potential energy, or does is this only how we define GPE?

[ThatLooksLikeARake]

may i ask why an externla force has to show up in the definition of GPE? why do we not consider the work done by gravity itself instead?

[homamhassn]

You said it is the work done by an external force so why when integrate you put the force of gravity

[CasperThePancake]

Hi there, I'm confused about something. In our example of an external force doing work on our objects to bring them from infinity to r, shouldn't this work be positive since the force and displacement vectors are in the same direction? This would be strange, since the derived formula is negative. Thanks for your help!

[lexanris]

Thanks for making this amazing video. Explanations very concise!
But i still have 1 query:

What I you understood is that Since GPE = -W by gravitational force to bring from infinity to r & W done by gravitational force in this case must >0 as the displacement is in same direction as force, GPE must be <0

But if you do this:
GPE = -W done by gravitational force to bring from infinity to r = - integral F dr … = GMm/r which is wrong

Why is it wrong only when i evaluate the integral?

I was just wondering abt this, hope it’s clear enough. Thanks in advance!

[rando_guy]

Hey, I'm hitting quite a roadblock when trying to derive the work done by gravity in bringing an object from infinity to r
this work done should in theory be equal to +GMm/r
but here's the derivation
both the gravitational force and dr (direction of instantaneous movement) are in the same direction
so it evaluates to the integral from infinity to r -> (GMm/r^2)dr = -GMm/r
this is so counter intuitive its crazy. like my instantaneous work done was positive and everything made sense but the limits just completely changed the game and made the result -ve
Is there any obvious mistake you can catch? it would be a ton of help

[metuphys]

thank you for the great explanation, although the video was pretty straight forward i may have missed something isn’t the work equal to Ep+Ek why did we ignore the kinetic energy of the planet? because the velocity of it was very low towards the begining? but as we approach to close distances that wont be the case any more so we cant ignore it. also didn’t we integrate from infinity to r, but the when he showed the graph of Force function it looked like we were integrating from r to infinity. i’ve been trying to derive this for 3 days and i tried to compute it like this: 0 to r(radius of earth) + r to some R (distance between moon and earth for example) im only a highschool student so im very new to this stuff i would be really happy if some one could tell me where was i wrong.

[dinogunjaca]

i was so hard at this you wouldant believe

[viradeus]

Great video. Perhaps you can derive GMm/r^2 as well?

[fazlerabby]

W=Fdxcos180 ;Fext.^dx =180 w=work done by external force but you didn’t write "cos180", why?

[physicshuman]

2:53

It’s not really the same it’s more of a continuous some of each single tiny step in height