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When you push your bicycle up on an inclined the potential energy of the bicycle and yourself increases. Where does this energy come from?

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When you walk up a hill, pushing a bicycle or not, you increase your potential energy by spending chemical energy. One of the reasons you need to eat is to ingest fuel, so to speak, that allows you to spend energy on doing your daily tasks. For example, your body can metabolize sugar (most notably glucose) by oxidizing it, which frees energy that you then can use (or store for later).

Maybe the situation is more clear if you think about a car driving uphill. Again, the potential energy is increased by spending chemical energy. Here, the source of energy may be more obvious: the combustion engine burns fuel (freeing chemical energy) to drive the cylinders, gears, and wheels.

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The sun gets its energy from the nuclear fusion, mainly the fusion of hydrogen atoms to form helium atoms.

This energy passes through the vacuum of space via Electromagnetic radiation.

Plants collect some of this radiation and use it to perform photosyntheses, which in turn is used to make carbohydrates and such.

You eat that plant or some other animal that has eaten that plant, using the carbohydrates energy to turn ADP (Adenosine diphosphate) into ATP (Adenosine triphosphate).

Your muscles turn that ATP back into ADP and in so doing are able to do the work of lifting yourself up the hill gaining potential energy.

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Gravitational potential is defined such that it is $0$ at infinity, and has negative values at all points other than the one at infinity. So, an object technically has the highest gravitational potential at infinity. (an extremely extremely far distance.)

The incline can be considered as path from an area of lower gravitational potential to a higher one. (since further distances have lesser negative value, i.e. higher potential.) Since the gravitational potential is increased in a process of sending the bike up the incline, the work done against the gravitational force to bring the bicycle up to the height is defined as the gravitational potential energy.

Technically you could consider the potential energy to be "stored" in the gravitational field between the Earth and the Bicycle. ( It arises due to the Kinetic Energy spent to lift the bike up the incline.)

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