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Physics Question - ma = mg
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Nominal Animal:

--- Quote from: bostonman on June 17, 2021, 03:46:30 am ---Unless you're talking about no air resistance.
--- End quote ---
That.

It is important to realize that having some force exist, does not mean energy is being spent/transferred.

In the case of a box sitting on the ground, the forces are static, and no energy is transferred.
Similarly, when the total forces acting on an object – including air resistance, gravity, everything – are equal, the object is in free fall, and retains its velocity.

For energy to be transferred via some force, the force has to do work.
thinkfat:
I don't think you need to dig deeply into Relativity to understand this equation. It's just a statement, an important one, though, expressed as a mathematical equation.

ma = mg just says that  mass behaves equally in a gravitational 'field' as when being accelerated by any force. The equation states that gravity can be understood as a force, causing a mass to accelerate.
Nominal Animal:

--- Quote from: Circlotron on June 17, 2021, 06:14:38 am ---Edit -> because your mass is now slightly more than 75kg then presumably your kinetic energy is also slightly more than 28,935 Joules.
--- End quote ---
Kinda, but also no (because you end up in a cyclical forever increasing mass and velocity argument if you follow that).

Kinetic energy isn't \$E_K = \frac{1}{2} m v^2\$, it is actually \$E_K = \frac{m c^2}{\sqrt{1 - \frac{v^2}{c^2}}}\$ for a rigid body.
The two agree for relatively small velocities \$v\$, but start to differ when velocity \$v\$ gets closer to the speed of light in vacuum \$c\$.
Here, \$m\$ is the rest mass, that is invariant of velocity.  This is based on the linear momentum as described by Einstein's theory of special relativity.

In practice, it means that given a specific kinetic energy, your velocity is smaller than the classical kinetic energy (\$E_K = \frac{1}{2} m v^2\$) would indicate; and given a specific velocity, your kinetic energy is higher than the classical formula suggests.

Special relativity describes two related concepts: invariant mass (the mass at rest, described by \$m\$ above), and relativistic mass which bends space-time.  It is easier to think of relativistic mass as relativistic energy, though, because us humans so closely associate "mass = weight"; and it really is the total energy, E, that bends space-time.  As an example, even though photons have no rest mass (\$m = 0\$), they do have linear momentum (as described in special relativity) and kinetic energy; and they do bend space-time.
bostonman:

--- Quote ---I don't think you need to dig deeply into Relativity to understand this equation. It's just a statement, an important one, though, expressed as a mathematical equation.

ma = mg just says that  mass behaves equally in a gravitational 'field' as when being accelerated by any force. The equation states that gravity can be understood as a force, causing a mass to accelerate.
--- End quote ---

I think I dug too deeply initially. When I saw this on TBBT, I initially thought it meant the Weight of (as an example) a box at rest on a table, and the table has an upward Force exerting a F=ma equal to the weight of the box W=mg.

After digging into it more, I began reading that they are equal because we are on Earth. This didn't make sense to me because a can be any object with acceleration that just so happens to be what the gravity is of that planet (or a point in space).

What I make of ma=mg is that an object sitting on the ground is experiencing a force F=ma where 'a' is Earth's gravity, and its weight is W=mg where 'g' is gravity on Earth; therefore ma = mg.

If we were on the moon, ma would also equal mg in the example above.
Ground_Loop:
Or, for the case originally cited, a = g. Something that given enough time, even Penny would have realized.
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