# Frictionless roller coaster

## Homework Statement

Consider a simple frictionless roller coaster. It begins from rest at x = 0 at a height of y = H. Then it drops into a dip, reaching a minimum at x = 100, with zero height (y = 0). Finally, it goes back up and reaches the crest of a small hill of height y = H/2 at x = 200. What can you say about the kinetic energy and gravitational potential energy of the roller coaster during its trip? Assume that the zero level of potential energy is taken to be y = 0.

x = 0 x = 100 x = 200 this is where the gravitational PE equals the kinetic energy
x = 0 x = 100 x = 200 this is where the kinetic energy equals the TOTAL energy
x = 0 x = 100 x = 200 this is where the gravitational PE is a maximum
x = 0 x = 100 x = 200 this is where the kinetic energy is a minimum
x = 0 x = 100 x = 200 this is where the kinetic energy is a maximum
x = 0 x = 100 x = 200 this is where the gravitational PE is a minimum

My answers are in bold, unfortunetly the program doesnt tell me which ones i got wrong, only that i got the problem wrong, i feel im close to the answer but dont know which one is wrong.

Thanks

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Doc Al
Mentor
x = 0 x = 100 x = 200 this is where the gravitational PE equals the kinetic energy
x = 0 x = 100 x = 200 this is where the kinetic energy equals the TOTAL energy
x = 0 x = 100 x = 200 this is where the gravitational PE is a maximum
x = 0 x = 100 x = 200 this is where the kinetic energy is a minimum
OK
x = 0 x = 100 x = 200 this is where the kinetic energy is a maximum
x = 0 x = 100 x = 200 this is where the gravitational PE is a minimum
OK

so the first one must be X=100 because PE and KE=0 at this point. I am still not sure what the second one is, i thought it was X=200, because its in motion but it says thats wrong.

Energy is always conserved, so if there PE=0 at the bottom of the run, what is the KE?

Have another a look at your 5th and 6th answers for a clue.

Doc Al
Mentor
so the first one must be X=100 because PE and KE=0 at this point.
How can they both be zero? That would mean the total energy is zero.
I am still not sure what the second one is, i thought it was X=200, because its in motion but it says thats wrong.
If KE = total energy, what must the PE be?

If KE = total energy, what must the PE be?
Zero, but im still unsure as to where PE would be zero, i thought it was at 100 but that doesnt seem to work...

Doc Al
Mentor
Zero, but im still unsure as to where PE would be zero, i thought it was at 100 but that doesnt seem to work...
Says who? PE is zero where y = 0.

Says who? PE is zero where y = 0.
so then would PE=KE=Total Energy? but i still dont see where PE would = KE,
Wait so at rest PE=KE=0=total energy at X=0 right? and gravitational PE= KE at X=100?

Doc Al
Mentor
so then would PE=KE=Total Energy? but i still dont see where PE would = KE
Not sure what you are saying here. PE + KE = Total Energy... always. So if PE = KE, then PE cannot also equal Total Energy (unless that's zero--not the case here).

If PE = KE, what must PE (and KE) be in terms of Total Energy?

So PE and KE would be the same in terms of total energy?

Doc Al
Mentor
So PE and KE would be the same in terms of total energy?
Analogy: If you and your brother have the same amount of money, how much do each of you have compared to the total?

Analogy: If you and your brother have the same amount of money, how much do each of you have compared to the total?
oh okay, half. But, i still dont understand when KE would = total energy since PE cannot be zero.

Doc Al
Mentor
But, i still dont understand when KE would = total energy since PE cannot be zero.
Why in the world do you think that PE cannot be zero? The problem even states:
Assume that the zero level of potential energy is taken to be y = 0.