Grav Potential Energy question doesn't make sense

[TrpnBils]

I'm missing something here...

Using the equation for calculating GPE, I'm getting an odd result in an example involving a roller coaster. Assuming at the top of the hill we have 100% PE and 0% KE and the reverse to be true at the bottom, we should have 0 joules of gravitational potential energy at the bottom of the hill, right?

If that's the case, and I'm trying to figure out the mass of the car, I can run it through the formula at various heights and get the same mass the whole way from the top to the bottom, except for where I have 0 Joules GPE. At that point it seems to turn to a mass of 0 kilograms.

What am I doing wrong here, because I know that's not right! It seems that even if the energy was all dispersed elsewhere (friction, etc) that there should still be a way to get the actual mass of the car with that equation...

 

[Pengwuino]

You need to provide more details. If you're saying that $PE = mgh$ should always give you the mass of the car, then yes it would except at the bottom of the roller coaster. The reason is not because the mass of the car has become 0 or something silly like that, it's the fact that your height has become 0.

 

[TrpnBils]

This is about the best I can do in MS Paint, but it should get the point across.

My point is, you should be able to get the same mass for all points involved since mass is irrelevant for conservation of energy (it cancels out with the ΔKE = ΔPE equation). You end up with an illogical answer at the last point there (E) because you've got zeroes in both the denominator and numerator (and would get the same thing in point A using the KE = 1/2 * m * v^2 equation).

Can mass be verified at that point if it's not given initially?

 

[Nabeshin]

This is about the best I can do in MS Paint, but it should get the point across.

My point is, you should be able to get the same mass for all points involved since mass is irrelevant for conservation of energy (it cancels out with the ΔKE = ΔPE equation). You end up with an illogical answer at the last point there (E) because you've got zeroes in both the denominator and numerator (and would get the same thing in point A using the KE = 1/2 * m * v^2 equation).

Can mass be verified at that point if it's not given initially?

You simply picked lousy coordinates for what you want to do. Redefine your zero point to be such that the height at the minimum is nonzero, say 1m.

 

[Psi^2]

In your equation you have zero over zero case, and that is indeterminate, so you cannot use that argument here.

For example:

0/0=x --> x*0=0

There is infinite solutions for x.

 

[TrpnBils]

You simply picked lousy coordinates for what you want to do. Redefine your zero point to be such that the height at the minimum is nonzero, say 1m.

But any object, at it's lowest point on a path, still has a mass, correct?

Likewise, look at the kinetic energy equation of k=1/2m*v²... if you have an object sitting still, it has no kinetic energy, but it still has a mass.

 

[sophiecentaur]

Where is your problem with the Mass?
It appears on both sides of the ΔPE=-ΔKE equation so it cancels out.