# Physics with Calculus/Mechanics/Energy

## Kinetic Energy

Kinetic energy is the energy of a mass in motion. In the non-relativistic approximation, kinetic energy is equal to

${\displaystyle K_{E}={\frac {1}{2}}mv^{2}}$
where m is the mass of the object and v is its velocity.

## Potential Energy

Potential energy in a constant gravitational field is given by:

${\displaystyle P_{E}=\ mgh}$
where m is the mass of the object, g is the strength of the gravitational field (${\displaystyle 9.8m/s^{2}}$ on earth) and h is the height of the object.

Work-Kinetic energy relation

${\displaystyle W=1/2mV_{F}^{2}-1/2mV_{I}^{2}}$

Potential energy, kinetic energy relationship

${\displaystyle K_{E}=P_{E},1/2mV^{2}=mGH}$

The law states that P_E (potential energy) is the energy of a given mass and position a certain amount of energy at such a height. When the object is in motion, K_E (kinetic energy), the potential energy is than transfered to kinetic energy. Since due to the third law of thermodynamics which states that energy can not be created nor destroyed, but only tranfered, such transfer of energy can occur

For a given equation, in order to figure out the work of the position, it can be done one of either two ways. The calculus method (which involves integration of the function) and the algebraic way (which involves the work kinetic energy relationship)

Calculus method (ex)-the compression of a spring from 1 m to 4 meters

Since integration basically finds the area of the given function (which can also be shown by the graph if possible). If F = Kx, where F is the force, K is the force constant, and x is the distance it was compressed. If the original function is F = Kx, since K is a constant, this than becomes K*(integral)X which then becomes K*x^2/2.

In order to figure out the work due to a changing amount of velocity, first determine how much "energy" is in the given system. Your equation from now on will be mgh + 1/2mV^2 = energy at full height.