OpenStudy (ghazi):

can anyone give me or show me how to prove weight= mass* gravity? please

5 years ago
OpenStudy (ghazi):

@experimentX

5 years ago
OpenStudy (experimentx):

are you trying to prove f=ma?

5 years ago
OpenStudy (ghazi):

no

5 years ago
OpenStudy (ghazi):

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

5 years ago
OpenStudy (experimentx):

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

5 years ago
OpenStudy (ghazi):

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

5 years ago
OpenStudy (ghazi):

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

5 years ago
OpenStudy (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.

5 years ago
OpenStudy (experimentx):

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

5 years ago
OpenStudy (experimentx):

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

5 years ago
OpenStudy (ghazi):

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

5 years ago
OpenStudy (anonymous):

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.

5 years ago
OpenStudy (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.

5 years ago
OpenStudy (anonymous):

I was writing it for 10 minutes and the page reloaded

5 years ago
OpenStudy (anonymous):

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.

5 years ago
OpenStudy (ghazi):

@ivanmlerner your explanation seems precised . thanks

5 years ago
OpenStudy (anonymous):

@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.

5 years ago
OpenStudy (ghazi):

agreed, but i'll get you that soon

5 years ago