Theoretically where the g factor came from? g=9.8

  • Context: Undergrad 
  • Thread starter Thread starter hagopbul
  • Start date Start date
  • Tags Tags
    G factor
Click For Summary

Discussion Overview

The discussion revolves around the theoretical origins of the gravitational acceleration factor, commonly denoted as g, which is approximately 9.8 m/s². Participants explore the relationship between g and fundamental concepts in physics, particularly Newton's laws and gravitational force, while also addressing the empirical nature of its measurement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that g is derived from Newton's laws of motion and gravitation, questioning how to theoretically derive g from these principles.
  • One participant presents the formula for gravitational force, indicating that g can be expressed as GM/r², where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center.
  • Another participant notes that the value of g is based on experimental measurements rather than theoretical derivation, emphasizing that it varies depending on location on Earth.
  • There is a discussion about the potential confusion between the symbol g and grams, with a preference expressed for using g or g0 to avoid ambiguity.
  • A participant mentions that the numerical value of g is arbitrary and depends on the units used for measurement, highlighting that it is not a universal constant.
  • One participant expresses difficulty in reconciling theoretical calculations with experimental values, indicating that their numbers do not match when applying Newton's laws.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the theoretical origins of g, with some emphasizing its empirical basis while others seek theoretical explanations. Multiple competing views remain regarding the derivation and understanding of g.

Contextual Notes

The discussion highlights the dependence on definitions and the variability of g based on location, as well as the unresolved nature of the calculations presented by participants.

hagopbul
Messages
397
Reaction score
45
to all

i need to know the theoretically where the g factor came from?
g=9.8
 
Physics news on Phys.org


hagopbul said:
to all

i need to know the theoretically where the g factor came from?
g=9.8

Hello hagopbul.What ideas or knowledge do you already have about g?
 


i think it is based on test only ... i tried to find some theoretical concept but i couldn't find any ...
 


Well, as g is the acceleration due to gravity, the two theories would be acceleration and gravity, both from Newton's laws. Can you think of a way to derive g from Newton's laws...?
 


The weight of an object = the gravitatonal force that the Earth exerts on the object = G m_earth m_object / r^2, where r is the dictance to the center of the earth, and G is the universal gravitational constant. Factor it like this: (G m_earth / r^2) m_object, and then everything in parentheses is "g". Therefore the weight of any object of mass m will be mg.
 


trying trough Newton but it is not working

the numbers are not matching
 


Show your calculation and the numbers you used.
 


Strictly speaking, it didn't come "theoretically" from anything- it came from experimentation. "9.98" is the measured acceleration, in meters per second squared, of an object at the Earth's surface. (Actually, 9.981 is a more accurate value- but the value varies from place to place on the earth.)

Given "[itex]F= GmM/r^2= mg[/itex], so that [itex]g= GM/r^2[/itex], we could then put r equal to the radius of the Earth and M equal to the mass of the earth, we could calculate g, but, in fact, it is done the other way around.
 


hagopbul said:
i need to know the theoretically where the g factor came from?
g=9.8

First...g is too easily mixed up with grams. I strongly prefer to use g or g0.
Second: g isn't 9.8. It's 9.8 m/s^2. The numerical value is completely arbitrary, and depends on the units you measure it in. 9.8 m/s^2, 32 ft/s^2, 71.3 gigafurlongs/fortnight^2...and it isn't any sort of universal constant. Earth's surface gravity is determined by how much matter has been piled into it and how close you are to said matter...Earth is a little lumpy and out of round, so that actually varies slightly depending on where you are. 9.8 m/s^2 is a common approximate value, and as stated, generally determined by measurement (it's much easier to measure gravitational acceleration than to directly measure Earth's mass and your distance from each particle of it).
 

Similar threads

  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 12 ·
Replies
12
Views
2K