Falling Bodies

What is the acceleration of a falling body?


Their Way

The formula for force is:


F = ma


The formula for the force of gravity is:


F
g = GMm  ⁄  r ²

The force acting on a falling body is the force of gravity. For a falling body, we have:



F = F
g

ma = GMm  ⁄  r ²

a = GM  ⁄  r ²


My Way
 

The formula for rest weight is:

RW = GMm  ⁄  r


The derivative of rest weight is:


DRW = −GMm  ⁄  r ²


The derivative of gravitational potential energy is:

DGPE = GMm  ⁄  r ²


The rate of change of energy of a falling body is zero. For a falling body, we have:

DKE + DGPE = 0


ma + GMm  ⁄  r ² = 0


a = −GM  ⁄  r ²


As a body falls to the ground, the displacement of the body from the Earth is decreasing. Meanwhile, the velocity of the body is increasing. When you have decreasing displacement and increasing velocity, you have negative acceleration.



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Here are their two formulas for force:

F = ma

Fg = GMm  ⁄  r ²

Both of those formulas are wrong. Here are the correct formulas:

DKE = ma

DGPE = GMm  ⁄  r ²

Force is a bunch of baloney.