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In a frictionless system, the prediction should be that the kinetic energy at the bottom of the hill will be equal to the potential energy at the top of the hill; however, it isn't a frictionless system. Energy is lost to friction (with the rails, with the air, etc.) between the top and bottom of the hill; therefore, some of the energy will be lost. Consequently, the most accurate prediction is b) About 70% of the `E_p` at the top.
As we do not have the lab data, we are unable to make specific calculations. I will make up some data to fill in the data we are missing.
We are given that:
m = 8260 kg
h = 35.5 m
L = 18.3 m
g = 9.8 m/s^2
`E_p=mgDeltah=(8260)(9.8)(35.5-0)= 2,873,654 J`
Let's say that it took t= 0.75s for the full length of the train to pass a point at the bottom of the hill; therefore,
`v = 18.3/0.75 = 24.4m/s`
Therefore, the percentage of `E_p` that is equal to `E_k` at the bottom of the hill is:
It is reasonable to expect that 14.4% of the potential energy was lost to friction.
The second question cannot be answered without having been on the ride.
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