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In summary, there are two equations for gravitational potential energy. The one you learned, MGH, is an approximation for objects close to the surface of the Earth. The other equation, GmM/r, is more accurate but more difficult to use. It is important to note that the "H" in the first equation should actually be "r," and the second equation does not have a squared term. This may have caused confusion with the force of gravity equation.

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the equation for gravitational potential energy you learned is an approximation that holds close to the surface of the Earth. The other one is more correct in general, though there should be no square on the bottom, but is a pain to use, so we only use it when we have to.

Consider... the word "height" does not make much sense for the distance from a sphere.

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Potential energy is the energy that an object possesses due to its position or state. It is often described as the stored energy in an object.

The most commonly used equation for potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance from a reference point.

There may be confusion over the potential energy equation because there are different forms of potential energy, such as gravitational potential energy, elastic potential energy, and electric potential energy, each with their own specific equation. Additionally, the equation may vary depending on the context or system being studied.

Yes, potential energy can be negative. This usually occurs when the reference point for measuring potential energy is chosen in a way that the object has a lower potential energy than at its current position. For example, an object close to the ground would have a negative gravitational potential energy if the reference point is chosen at a higher position.

Potential energy and kinetic energy are both forms of energy, and they are often interchanged through processes such as work and energy transfer. Potential energy can be converted into kinetic energy, and vice versa. For example, when an object falls, its potential energy decreases while its kinetic energy increases.

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