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22 gru 2020 · Gravitational potential energy (GPE) is an important physical concept that describes the energy something possesses due to its position in a gravitational field. The GPE formula GPE = mgh shows that it depends on the mass of the object, the acceleration due to gravity and the height of the object.
Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity. If the body has a mass of 1 kilogram, then the potential energy to be assigned to that body is equal to the gravitational potential.
The change in gravitational potential energy \(\Delta PE_g\), is \(\Delta PE_g = mgh\), with \(h\) being the increase in height and \(g\) the acceleration due to gravity. The gravitational potential energy of an object near Earth’s surface is due to its position in the mass-Earth system.
Potential energy is particularly useful for forces that change with position, as the gravitational force does over large distances. In Potential Energy and Conservation of Energy, we showed that the change in gravitational potential energy near Earth’s surface is \[ \Delta U = mg(y_2− y_1) \label{simple}\]
The general form of the gravitational potential energy of mass m is: where G is the gravitation constant, M is the mass of the attracting body, and r is the distance between their centers. This is the form for the gravitational potential energy which is most useful for calculating the escape velocity from the earth's gravity. Index Energy concepts
Starting from the escape velocity formula, derive an equation for the radius of the event horizon in terms of m (the mass of the black hole), G (the gravitational constant), and c (the speed of light).
gravitational potential energy = mass × height × gravitational field strength (g)
