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I just need to check if my understanding of the transfer of gravitational potential energy to kinetic energy is correct. Is anything wrong below?

Say if a body were suspended at a height h above the surface. It has potential energy $E_P=mgh$. When the body is released from this height, the potential energy is transferred into kinetic energy $E_K=\frac12 mv^2$.

$$mgh = \frac12mv^2$$ $$gh = \frac12v^2$$ $$2gh = v^2 $$ $$v = \sqrt{2gh}$$

Is this saying for any object (ignoring the effects of drag) its velocity is the same?

Factoring in drag, we know that drag $\propto$ velocity$^2$. So if the object (falling from the same height) has a greater surface area/size, its drag will be greater and velocity will be less.

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Yes, two objects with the same shape but different masses will have the same velocity after being dropped from the same height.

Galileo tried this a while ago by dropping two such objects from a tower.

Factoring in drag, we know that drag ∝ velocity2. So if the object (falling from the same height) has a greater surface area/size, its drag will be greater and velocity will be less.

And with that you have proven that your model of all potential energy being transformed into kinetic energy does not hold in that case. Some Energy is required to "push" the air to the side. If the shapes of the objects are different, it will take different amounts of energy to push the air out of their way, thus the kinetic energy left will be less.

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I just need to check if my understanding of the transfer of gravitational potential energy to kinetic energy is correct. Is anything wrong below?

Yes. Gravity is not a force in the Newtonian sense. The potential energy of the body isn't stored in the gravitational field or the Earth, it's in the body itself, in its mass-energy. When you drop the body the potential energy gets converted into kinetic energy, and the mass reduces. When you radiate the kinetic energy away, you're left with a mass deficit, see Wikipedia. So $E_P=mgh$ and $E_K=\frac12 mv^2$ are a little misleading.

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