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Physics Question - ma = mg

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bostonman:
I'm trying to understand exactly why ma = mg.

I took physics, and, the concept of weighing myself on the scale and learning it's really our mass, I'm confused about ma = mg (this began after watching the Big Bang Theory).

If my body mass is 75kg, and I get on a scale, my 'weight' is (75 * 9.8): 735N

If something with a mass of 75kg accelerates at 9.8, then the 'force' is also 735N

Obviously ma = mg in this case. After reading, it's equal because we are on Earth. If I weighed myself on the moon, then ma = mg, however, if everything is relative to gravity on the moon, then ma = mg on the moon. For the most part, ma would equal mg anywhere in the universe providing gravity and acceleration are the same.

Am I missing something in the translation of why ma = mg?

Whales:
Algebra:
m = mass
a = acceleration
g = acceleration due to gravity ~= 9.8ms-2 on earth's surface

ma = mg

Divide both sides by m:

a = g

Yep.  Don't think of g as a variable, but instead an exact value.  Just like pi isn't a variable, it's a value, even though we write it as π instead of 3.14159265.   I can write y = π and I can write a = g; these are both choices I make of subbing in particular values for particular purposes.

g on the moon != g on earth, they're completely different values and hence once subbed in the meaning of the equations gets limited to "only valid on X planet's surface".  Just like how if I choose m=70kg then the above equation becomes "only valid for human beings" instead of "valid for everything with a mass in a gravitational field".

Does this help, or am I going down completely the wrong path?

andy3055:
Here is a good page to read (ThoughtCo.com): https://www.thoughtco.com/mass-and-weight-differences-606116

bostonman:

--- Quote ---g on the moon != g on earth, they're completely different values and hence once subbed in the meaning of the equations gets limited to "only valid on X planet's surface".
--- End quote ---

That was my point. My 'mass' (using 75kg) is the same throughout the universe and can't change (unless I eat lots of food while venturing around space). a = g doesn't only exist on Earth, but can exist anywhere in the universe too.

So saying because we are on Earth, and acceleration due to gravity is 9.8, then ma = mg, isn't really correct.

CatalinaWOW:

--- Quote from: bostonman on May 13, 2021, 03:38:12 am ---
--- Quote ---g on the moon != g on earth, they're completely different values and hence once subbed in the meaning of the equations gets limited to "only valid on X planet's surface".
--- End quote ---

That was my point. My 'mass' (using 75kg) is the same throughout the universe and can't change (unless I eat lots of food while venturing around space). a = g doesn't only exist on Earth, but can exist anywhere in the universe too.

So saying because we are on Earth, and acceleration due to gravity is 9.8, then ma = mg, isn't really correct.

--- End quote ---

You are right.  The equality is not general, it only holds for the special case where a=g.  That special case does apply almost universally on this planet and as far as we know no one lives anywhere else (space station visits not counting as living), so you can see where someone got a little ahead of themselves with this one.