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comment Can a car get better mileage driving over hills?
@Edward, your claim that the gravitational potential energy sums to zero can be challenged on earth. After ascending a hill, you can not get all that stored up energy back as it will be consumed by increased air friction or brake heat on the way down, thus not being used fully to propel the car. You will be overcoming more gravity on the way up than you can consume on the way down. I would say that calling it a zero sum is valid only in a vacuum. This may be a large enough discrepancy in your logic to sway the conclusion.