Potential Energy question Confusion on the sign

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Here is my question.

For example if i am standing on top of the empire state building and i define that to be height=0 and i define the downward direction to be positive. if i drop a mass does its potential energy increase based on my definition of direction?

My actual problem was an exam question we were asked to find the equation of motion of atwoods machine using energy conservation.

the way i defined it on the exam is the same way i described it previously. and instead of getting x(dbl dot) = g(m1-m2)/(m1+m2)

i came up with an extra minus sign in front of the g in the numerator....

is this wrong. should the equation of motion come out the same no matter how you define your directions ( as long as you are consistent)
Also does kinetic energy depend on this sign definition

it shouldnt, kinetic energy is always positive....
In answer to your first question, the formula [Potential Energy= mgh] only works when you make h= altitude and you ignore all other forces. If you are going to change that, you need to move to a general form of the potential energy equation.

For your second question, KE=[itex]\frac{1}{2}[/itex]mv2, with M≥0, there is no way KE≤0.
This dosent make sense to me.

i didn't change the problem i just flipped it b.c it was more convenient i don't understand why its different now.

instead of one Mass 1 PE increasing, it decreases.


instead of Mass 2 PE decreasing, it increases.

i dont know anything anymore...
The Reason you're getting incorrect answers is that you are using a simplified version of the Potential Energy equation that is only valid under certain conditions. The equation you are probably using for Potential Energy is:

Where: m= mass , g= acceleration due to gravity (9.8 m/s/s) , h= height off of the ground.

However, that is not a general equation for potential energy. That equation only works if:
a) Height is distance from the ground
b) You are not considering any other forces.

If you chance either one of those (i.e., changing your coordinates so H no longer equals height from the ground), you have to stop using the PE=mgh equation and start using the general equation for Potential Energy, which is detailed here: http://en.wikipedia.org/wiki/Potential_energy

The general form of the PE equation is considerably more complicated, so it would probably be easier to stick with the PE=mgh form and not to set H=0.

EDIT: Looking back on your original question, I noticed the last part regarding Equations of Motions I didn't see before. I could be mistaken, but I believe equations of motion should be the same if you change directions, but not if you change reference frames, though I am not positive of that.

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