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C O N T E N T S:

- The zero of gravitational potential energy can be chosen at any point (like the choice of the zero of a coordinate system), the potential energy at a height h above that point is equal to the work which would be required to lift the object to that height with no net change in kinetic energy.(More…)

**KEY TOPICS**

** The zero of gravitational potential energy can be chosen at any point (like the choice of the zero of a coordinate system), the potential energy at a height h above that point is equal to the work which would be required to lift the object to that height with no net change in kinetic energy.** [1] What is best way to explain the negative signs in work, potential energy, absolute gravitational potential energy, and gravitational potential. [1] Therefore, we can define the difference of elastic potential energy for a spring force as the negative of the work done by the spring force in this equation, before we consider systems that embody this type of force. [2] The total potential energy of the system is the sum of the potential energies of all the types. (This follows from the additive property of the dot product in the expression for the work done.) [2] Let’s look at some specific examples of types of potential energy discussed in the section on Work. [2] It has to be positive, otherwise the potential energy would be larger closer to the Earths center – but that does not work with where the kinetic energy came from. [1] After integration, we can state the work or the potential energy. [2]

E mgh (where E is the potential energy, m is mass and h is the vertical distance from the massive object). [1] According to current literature, gravitational energy is the potential energy a body with mass has in relation to another massive object due to gravity. [1] The potential energy difference depends only on the initial and final positions of the particles, and on some parameters that characterize the interaction (like mass for gravity or the spring constant for a Hooke’s law force). [2] By choosing the conventions of the lowest point in the diagram where the gravitational potential energy is zero and the equilibrium position of the spring where the elastic potential energy is zero, these differences in energies can now be calculated. [2] Let’s look at a specific example, choosing zero potential energy for gravitational potential energy at convenient points. [2] Often, the ground is a suitable choice for when the gravitational potential energy is zero; however, in this case, the lowest point or when h 0 is a convenient location for zero gravitational potential energy. [2] Can we use this to determine some form of “gravitational potential energy in a point”? I claimed earlier that we cant, but mathematically speaking, we can actually do that. [1] As long as there is no friction or air resistance, the change in kinetic energy of the football equals the change in gravitational potential energy of the football. [2] Since the force required to lift it is equal to its weight, it follows that the gravitational potential energy is equal to its weight times the height to which it is lifted. [1] Since U depends on x 2, the potential energy for a compression (negative x) is the same as for an extension of equal magnitude. [2] Gravitational energy (which is a form of potential energy which an object possess when it is in a gravitational field) is usually described as negative, but that is actually not very relevant. [1] Current literature rationalize that by saying the gravitational fields have negative energy when they try to explain gravitational potential energy. [1]

This is especially true for electric forces, although in the examples of potential energy we consider below, parts of the system are either so big (like Earth, compared to an object on its surface) or so small (like a massless spring), that the changes those parts undergo are negligible if included in the system. [2] If the spring force is the only force acting, it is simplest to take the zero of potential energy at x 0, when the spring is at its unstretched length. [2] The equilibrium position of the spring is defined as zero potential energy. [2] Therefore, based on this convention, each potential energy and kinetic energy can be written out for three critical points of the system: (1) the lowest pulled point, (2) the equilibrium position of the spring, and (3) the highest point achieved. [2] The block started off being pulled downward with a relative potential energy of 0.75 J. The gravitational potential energy required to rise 5.0 cm is 0.60 J. The energy remaining at this equilibrium position must be kinetic energy. [2] This loss in kinetic energy translates to a gain in gravitational potential energy of the football-Earth system. [2] Therefore, energy is converted from gravitational potential energy back into kinetic energy. [2] The elastic potential energy of the spring increases, because you’re stretching it more, but the gravitational potential energy of the mass decreases, because you’re lowering it. [2] The gravitational potential energy is higher at the summit than at the base, and lower at sea level than at the base. [2] Gravitational potential energy is only defined up to an additive constant. [1] A simple system embodying both gravitational and elastic types of potential energy is a one-dimensional, vertical mass-spring system. [2] We consider various properties and types of potential energy in the following subsections. [2] For each type of interaction present in a system, you can label a corresponding type of potential energy. [2] Each of these expressions takes into consideration the change in the energy relative to another position, further emphasizing that potential energy is calculated with a reference or second point in mind. [2] The lowest height in a problem is usually defined as zero potential energy, or if an object is in space, the farthest point away from the system is often defined as zero potential energy. [2] Notice how we applied the definition of potential energy difference to determine the potential energy function with respect to zero at a chosen point. [2] The numerical values of the potential energies depend on the choice of zero of potential energy, but the physically meaningful differences of potential energy do not. [2] The equilibrium location is the most suitable mathematically to choose for where the potential energy of the spring is zero. [2] We need to pick an origin for the y-axis and then determine the value of the constant that makes the potential energy zero at the height of the base. [2] As the object falls and gains speed (and thus kinetic energy), it has to lose potential energy if the sum of the energies of the object is to be constant. [1] Some of these are calculated using kinetic energy, whereas others are calculated by using quantities found in a form of potential energy that may not have been discussed at this point. [2] This property allows us to define a different kind of energy for the system than its kinetic energy, which is called potential energy. [2] View this simulation to learn about conservation of energy with a skater! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. [2] Therefore, we need to define potential energy at a given position in such a way as to state standard values of potential energy on their own, rather than potential energy differences. [2] This formula explicitly states a potential energy difference, not just an absolute potential energy. [2] When the spring is expanded, the spring’s displacement or difference between its relaxed length and stretched length should be used for the x-value in calculating the potential energy of the spring. [2] Assuming the spring is massless, the system of the block and Earth gains and loses potential energy. [2] We draw the conclusion that the rock has lower potential energy if it is closer to the Earths center (or whatever source of gravity we are looking at). [1] Because of the inverse square nature of the gravitational force, the force approaches zero for the large distances (infinity) and hence it is appropriate to choose the zero of the gravitational potential energy at an infinite distance. [1] Let’s choose the origin for the y-axis at base height, where we also want the zero of potential energy to be. [2] It is important to remember that potential energy is a property of the interactions between objects in a chosen system, and not just a property of each object. [2] Notice that the potential energy, as determined in part (b), at x 1 m is U(1 m) 1 J and at x 2 m is U(2 m) 8 J; their difference is the result in part (a). [2] Conventionally one defines this constant so that the potential energy vanishes at spatial infinity. [1]

Kinetic – energy of motion – rock rolling down hill Potential – ability to do work in future – rock at the top of a hill or a fluid has it under pressure. [3]

**RANKED SELECTED SOURCES**(3 source documents arranged by frequency of occurrence in the above report)

1. (38) 8.1: Potential Energy of a System – Physics LibreTexts

2. (14) Why is gravitational potential energy negative? – Quora

3. (1) [PDF] Force of B on A ~ q A x q B – Free Download PDF