The First Law of Thermodynamics

noneThe First Law Of Thermodynamics:

�Energy can be changed from one form to another, but it can not be created or destroyed.�

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So, after taking thermodynamics into account we see that at any given point during the roller coasters ride, (granted we are using a traditional roller coaster in which there are no extra chains, or engines to lift it other than the first hill, and that friction is negligible) we see that:

Kinitial+Uinitial=Kfinal+Ufinal

Now, with a little algebra, and an initial velocity of 0, that the equation becomes:

v=(2g(hinitial-hfinal)½

or that:"velocity equals the square root of 2 times gravity times the difference in height"

It is because of this correlation between kinetic and potential energy which explains whey roller coasters never exceed the height of their first hill. Notice, that if a height of a hill is equal to the first hill height, hinitial-hfinal=0 and so v=0, or there is no movement, so all hills have to be smaller than the first hill. Also notice, that if the second hill is larger than hinitial-hfinal will be negative, and since we can't take the square root of a negative without using imaginary numbers, this too is not possible.

The First Law Of Thermodynamics:

�Energy can be changed from one form to another, but it can not be created or destroyed.�

click here to see the source page.

So, after taking thermodynamics into account we see that at any given point during the roller coasters ride, (granted we are using a traditional roller coaster in which there are no extra chains, or engines to lift it other than the first hill, and that friction is negligible) we see that:

Kinitial+Uinitial=Kfinal+Ufinal

Now, with a little algebra, and an initial velocity of 0, that the equation becomes:

v=(2g(hinitial-hfinal)½

or that:"velocity equals the square root of 2 times gravity times the difference in height"

It is because of this correlation between kinetic and potential energy which explains whey roller coasters never exceed the height of their first hill. Notice, that if a height of a hill is equal to the first hill height, hinitial-hfinal=0 and so v=0, or there is no movement, so all hills have to be smaller than the first hill. Also notice, that if the second hill is larger than hinitial-hfinal will be negative,