Treadmill vs. Real Hill: Which is harder to run

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Thanks to Galilean relativity it should be just as hard to run on an inclined treadmill as it is to run on a hill of the same incline. But you don't gain gravitational potential energy on a treadmill, so can it really be true?

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0:00 Introduction
2:50 Building the vehicle
3:28 Components of the car
4:41 Galilean relativity
5:55 Train analogy
9:42 Infinite ladder analogy
11:22 Ladder experiment
14:30 What about energy?!
15:15 Leg muscles
15:52 The experiment
17:56 The data
18:31 Flat Earth parody
21:07 Analysing the data
25:37 Sponsor message