Can You Explain the Mystery of 9.8m/s^2 Acceleration on Earth?

[Theonefrom1994]

TL;DR Summary

How did people find 9.8m/s^2 If there’s air resistance on earth ?

My understanding is that all falling objects on Earth will fall at the same acceleration of 9.8m/s^2 in the absence of air resistance . But isn’t air resistance everywhere on the planet since we have an atmosphere ? . So how did these scientists from back in the day figure out the 9.8 number ?

 

[PeroK]

Summary:: How did people find 9.8m/s^2 If there’s air resistance on Earth ?

My understanding is that all falling objects on Earth will fall at the same acceleration of 9.8m/s^2 in the absence of air resistance . But isn’t air resistance everywhere on the planet since we have an atmosphere ? . So how did these scientists from back in the day figure out the 9.8 number ?

Someone has written a book about it:

https://www.springer.com/gp/book/9783319749587

 

[DaveE]

It's a good question. However, there are many circumstances where air resistance only creates small errors. For example, dropping small dense objects, like an iron ball.

 

[Vanadium 50]

I like PeroK's answer. However, the question assumes, as Perry Mason would say "facts not in evidence". Galileo's suggestion that bodies accelerate at the same rate was proposed in 1638 and the vacuum pump was invented in 1650.

Furthermore, one can do this measurement today without a vacuum. Take a pendulum with bobs of fixed size and shape, but of different materials. Plot g vs 1/m and extrapolate to zero.

 

[Theonefrom1994]

I like PeroK's answer. However, the question assumes, as Perry Mason would say "facts not in evidence". Galileo's suggestion that bodies accelerate at the same rate was proposed in 1638 and the vacuum pump was invented in 1650.

Furthermore, one can do this measurement today without a vacuum. Take a pendulum with bobs of fixed size and shape, but of different materials. Plot g vs 1/m and extrapolate to zero.

I was trying to know how people figured it out because it was never presented to me . I’ was sure there evidence for it I was just unaware Of what that evidence is And how it can be demonstrated if you don’t have a vacuum .

 

[PeroK]

I was trying to know how people figured it out because it was never presented to me . I’ was sure there evidence for it I was just unaware Of what that evidence is And how it can be demonstrated if you don’t have a vacuum .

Suppose we have a pendulum and we count the time for a large number of oscillations. If air resistance is significant then by doubling the density of the bob (with the same size and shape) we should get a significant change in the time for the heavier bob - significantly less. If, however, we get almost the same time for both bobs, then air resistance must be almost negligible. Hence the time must be close to what we would get in a vacuum, and we can get an accurate estimate for $g$.

 

[sophiecentaur]

because it was never presented to me

Your question shows that you were actually thinking about the problem. Much of the Science we are taught at elementary level is not suitable for too much follow-up thinking.
Keep reading and asking.

 

[ZapperZ]

I was trying to know how people figured it out because it was never presented to me . I’ was sure there evidence for it I was just unaware Of what that evidence is And how it can be demonstrated if you don’t have a vacuum .

Do this in air then. For small oscillation, the affect of air is negligible, y'know, the effect is so small it is in the high decimal digits.

We do this in many General Physics lab. Measure the period T of a pendulum at a particular length L. Then vary L, measure T again... You will have a series of values of T for each L.

Now plot T versus √L. You will find that it resembles a straight line. Do a linear fit through the data points. The slope of your graph is equal to 2π/(√g). This means that knowing the slope of your fitted line, you now can experimentally find g!

I've just done my students' next week's lab!

Zz.

 

[Theonefrom1994]

Thanks for the responses ! This was helpful ! I’ll try to do my own set up with a pendulum and try this out !

 

[Meir Achuz]

Physical constants are often defined in one way, but best measured in a different way.

 

[Lnewqban]

This is a really good question.

I just learned that Wikipedia shows some interesting responses to it:
https://en.m.wikipedia.org/wiki/Galileo_Galilei#Falling_bodies

https://en.m.wikipedia.org/wiki/Standard_gravity