why we use g=10m/s²
Answers
Answer:
Why do we use g=10m/s2?
Actual Newton´s Law of universal gravitation states that a mass particle attracts any other particle of mass with a force that is directly proportional to their multiplied masses and inversely proportional to the squared distance between them.
That is, F=G m1*m2/d²For the case you propose, we are considering one of the “particle” masses to be that of Earth and the other to be any object near enough its that we could find the force with which Earth attracts objects near it to be simplified to F=g*m2, g standing for G*m1/d².
Earth´s mass equals 5,9722 E24 kg
Earth´s mean radius equals 6,371 E06 m
G, a gravitation constant, actually exists merely to translate the value in units kilograms²/meters² to Newtons. G=6,674 E-11
Multiplying them accordingly will result g=9,8198.
But, since we only know G to the 4th significant figure, we, then, are only allowed to express it to the 4th figure as well. Hence, g=9,820
So, every time you take g to be 10m/s² you are making a known mistake of 18 parts per thousand (1000–982). Pretty negligible since most stopwatches will measure free falling bodies with 3 significative.
As a curiosity, g=10m/s² is valid for a line some 65m underground the equator.
As a tradition in the realm of exact sciences I will leave to the reader the task of quantifying how far up from Earth´s surface will this evaluation hold. :D
Explanation: