Potential energy is the energy due to position, composition, or arrangement. Also, that is the energy associated with forces of attraction and also repulsion in between objects. Any object that is lifted from its resting position has stored energy because of this it is referred to as potential energy since it has actually a potential come do work when released.

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Introduction

For example, as soon as a sphere is exit from a certain height, it is pulled by gravity and also the potential energy is convert to kinetic energy throughout the fall. Together this energy converts indigenous potential come kinetic, that is necessary to take into factor to consider that energy cannot be created nor destroyed (law of conservation of energy). This potential power becomes kinetic power as the ball accelerates towards the ground. The object"s complete energy have the right to be found through the amount of this to energies.

In one exothermic bsci-ch.orgical reaction, potential power is the source of energy. During an exothermic reaction bonds rest and brand-new bonds type and protons and also electrons go from a framework of higher potential power to lower potential energy. During this change, potential power is convert to kinetic energy, which is the warmth released in reactions. In an endothermic reaction the opposite occurs. The protons and also electrons move from one area of low potential power to an area of high. This takes in energy.

Potential power on a molecule level: Energy save in bonds and static interactions are:

Covalent binding Electrostatic pressures Nuclear forces

Gravitational Potential Energy

\

where \(F\) is the the opposite force and \(x\) is the street moved. To calculation the potential energy of an object on planet or within any other force field the formula

\

with

\(m\) is the mass of the thing in kilograms \(g\) is the acceleration due to gravity. On planet this is 9.8 meters/seconds2 \(h\) is the object"s height. The elevation should it is in in meters.

If the units above are supplied for the \(m\), \(g\), and also \(h\), climate the final answer have to be given in Joules.


Example \(\PageIndex1\)

A 15 gram sphere sits on height of a 2 m high refrigerator. What is the potential energy of the round at the peak of the refrigerator?

Solution

Use Equation \refpe1 with \(m =15\, grams\). This mass yet has to be in kilograms. The conversion come grams come kilograms is: 1,000 grams per 1 kg

\(\textheight=2\, m\) \(g=9.8 \, m/s^2\)

\


Example \(\PageIndex2\)

What is the massive of a cart full of groceries that is sitting on top of a 2 m hill if its gravitational potential power is 0.3 J?

Solution

Use Equation \refpe1

\<0.3\,J=(m)(9.8\, m/s^2)(2\,m) \nonumber\>

and deal with for mass

\


Example \(\PageIndex3\)

A 200 gram load is put on optimal of a shelf with a potential power of 5 J. Just how high is the load resting?

Solution

\<5\,J=\left(\dfrac200\,g1000\,g/kg\right)(9.8 m/s^2)(h) \nonumber\>

and settle for height

\


Coulombic Potential Energy

The potential energy of two charged corpuscle at a distance have the right to be found through the equation:

\

where

\(r\) is distance \(q_1\) and \(q_2\) space the charges \(ε_0= 8.85 \times 10^-12 C^2/J\,m\)

For charges with the exact same sign, \(E\) has a + sign and also tends to acquire smaller together \(r\) increases. This can define why favor charges repel each other. Systems like a low potential energy and thus defeat each various other which boosts the distance between them and also lowers the potential energy.

*

For charges with different charges, the contrary of what is stated above is true. E has actually a - authorize which i do not care even more negative as the opposite charged particles attract, or come closer together.

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Example \(\PageIndex5\)

Find the distance in between two particles that have actually a potential power of \(0.2\, J\) and also charges that \(2.5 \times 10^-6\, C\) and \(3.1 \times 10^-6\, C\).

Solution

\<\beginalign* 0.2 &=\dfrac(2.5 \times 10^-6\,C)(3.1 \times 10^-6 \,C)4\pi (8.85 \times 10^-12 \,C^2/Jm) r \\<4pt> &=\dfrac(8.99 \times 10^9)(7.75 \times 10^-11)r \\<4pt> &=\dfrac0.6967r \endalign*\>