General > General Technical Chat

Physics Question - ma = mg

<< < (5/33) > >>

JohnnyMalaria:

--- Quote from: IanB on May 13, 2021, 04:10:40 am ---
--- Quote from: Whales on May 13, 2021, 03:55:57 am ---
--- Quote from: bostonman on May 13, 2021, 03:38:12 am ---So saying because we are on Earth, and acceleration due to gravity is 9.8, then ma = mg, isn't really correct.

--- End quote ---

It is correct, but only in certain situations.  Basically no equation is truly universal, all have limitations.

   f = ma  <-- only directly usable as an approximation between a very large mass (earth) and a very small mass (eg a person) OR between two very distant bodies where their radii are much less than their seperatory distance.  Otherwise the results are quite wrong (you have to break each mass down into smaller pieces & integrate the results instead).

--- End quote ---
Excuse me? F = ma is one of the fundamental laws of Newtonian mechanics. It is always exactly true, without exception, in a Newtonian framework. What makes you think it is an approximation?

--- End quote ---

Your own assertion answers your question :)

It's an approximation because it's only "exactly true" "in a Newtonian framework". Ergo, it's an approximation because it fails outside of a Newtonian framework.

mathsquid:

--- Quote from: AntiProtonBoy on May 14, 2021, 01:32:52 am ---Also, how do I insert LaTeX formulas in this forum?

--- End quote ---

To do displayed math, just put it between double dollar signs. I don't know if there's a way to do it inline.

bostonman:
I'm somewhat glad my question wasn't so easily answered because I thought it was too simple. As someone pointed out above, some of this has deviated and dove deep into physics.

Although the basic plug and chug formulas make things easy, sometimes they don't make sense after trying to analyze them.

One thing we can all agree on is mass remains constant, it can't change throughout the universe. If I want to know my weight on Earth, using 100kg for Mass to make the math easier, then (W= mg) it's 9.8 * 100kg = 980N. If a 100kg object accelerates at 9.8m/s^2 for 1s, then the Force (F = ma) would also be 980N.

Therefore ma = mg.

Now take the same situation above and place me on the moon. My weight is 162N (moon gravity = 1.62m/s^2) and the 100kg object accelerating at 1.62m/s^2 for 1s is also 162N.

Therefore ma = mg.

My point is: from my understanding, no special case exists where ma = mg because we are on Earth. From my initial assumption, it seemed a special case existed where ma = mg because we are on Earth and/or a connection existed with 9.8 to make ma = mg.

Basically, they can equal each other anywhere in the universe providing the accelerating object accelerates at the same rate as the gravity as to where you are.

I don't want to deviate, but I'm a bit uncertain how F=ma and W=mg were discovered. We can calculate Mass because we know gravity, but centuries ago, nobody knew the acceleration of gravity, so they couldn't calculate the Mass being dropped. It's kind of the chicken or the egg I guess.

Also, if I place a 100kg block on a table, is the block a Weight with the table acting as a Force in the upward direction, or is the block also a Force? During this discussion, I began realizing, I'm confused as to when to use a Weight and when to use a Force (unless we are talking about say a car driving into an object, then that's a Force).

For reference, at 5:20 is where the original question (from The Big Bang Theory) came from:

AntiProtonBoy:

--- Quote from: mathsquid on May 14, 2021, 02:02:43 am ---To do displayed math, just put it between double dollar signs. I don't know if there's a way to do it inline.

--- End quote ---

Inline test: \$ foo = x \$

$$ foo = x^6 $$

Edit: looks like inline uses the slash dollar sign syntax.
Also LaTeX doesn't work when previewing the post. Dave, is there way to fix this?

Alex Eisenhut:

--- Quote from: bostonman on May 14, 2021, 03:13:53 am ---
One thing we can all agree on is mass remains constant, it can't change throughout the universe.

--- End quote ---

Not sure that's correct. There's rest mass and relativistic mass.

https://en.wikipedia.org/wiki/Mass_in_special_relativity

Navigation

[0] Message Index

[#] Next page

[*] Previous page

There was an error while thanking
Thanking...
Go to full version
Powered by SMFPacks Advanced Attachments Uploader Mod