## ghazi 3 years ago can anyone give me or show me how to prove weight= mass* gravity? please

1. ghazi

@experimentX

2. experimentX

are you trying to prove f=ma?

3. ghazi

no

4. ghazi

i am thinking and striving to prove weight = mass*gravity? how, i was pondering over it

5. experimentX

this comes from definition ... weight = gravitational force. weight = GmM/R^2 = m GM/R^2 = mg

6. ghazi

this is my question how weight = gravitational force* mass (not weight @experimentX :) )

7. ghazi

and i heard that there is a long proof of it i am looking for that

8. experimentX

weight = gravitation force = m g ---------------------------- well i guess there is since there is lot's of confusion around mass since the definition of mass keeps going round and round around force and inertia. I haven't understood it correctly.

9. experimentX

probably to clear out this circular logic of mass. but weight = mg ... this comes from newton's second law.

10. experimentX

weight= mass* acceleration due to gravity ------------------------------------- probably you made mistake here ... gravity would mean different thing.

11. ghazi

@experiment i need mathematical explanation of this definition how weight = mass*gravity?

12. Carl_Pham

There is no mathematical derivation. That the force exerted by gravity on an object is proportional to its mass is a hypothesis of Newtonian gravitation, confirmed by experiment. It's an observation, not a deduction.

13. ghazi

@carl_pham everything in this universe has a mathematical explanation and i strongly believe it has some mathematical explanation and it is in the book principia mathematica by newton , albeit i tried hard to understand that but unfortunately i couldn't and once again i must say there is a derivation of this but unfortunately i am unable to find it.

14. ivanmlerner

I was writing it for 10 minutes and the page reloaded

15. ivanmlerner

The thing is, \[F=ma=mGMr^{-2}\]if we notice that we are considering the weight only for objects very close to the surface of the earth, we see that GMr^-2=g and even though this radius usually change, we can consider it as constant and equal to the radius of the earth, therefore getting the acceleration g. A more formal explanation involves the same concept, we take a taylor expansion around the radius of the earth of the function GMr^-2=g(r) and consider only the first term since we r and the radius of the earth are very close. This provides a more clear view of whats going but is really unnecessary. It is not useful to continue the taylor expansion to include greater heights because the function F is really simple.

16. ghazi

@ivanmlerner your explanation seems precised . thanks

17. Carl_Pham

@ghazi, and interesting faith, but unfortunately you are wrong. Anything derived purely from empirical observation has no mathematical derivation at all. It just is. Obvious examples include the value of the fine structure constant, as well as many other important constants, why the nuclear forces have a finite range, and the Second Law of thermodynamics (the one that says the entropy of the universe is always increasing). Not one of these things has a mathematical, or indeed any explanation. They are simply observable facts that characterize this universe.

18. ghazi

agreed, but i'll get you that soon