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

$K_{E}={\frac {1}{2}}mv^{2}$

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:

$P_{E}=\ mgh$

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

Work-Kinetic energy relation

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

Potential energy, kinetic energy relationship

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

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 then transfered to kinetic energy. Due to the third law of thermodynamics, which states that energy can not be created or destroyed, but only tranferred, such transfer of energy can occur.

For a given equation, figuring out the work of the position can be done in one of 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 then 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. The equation from now on will be mgh + 1/2mV^2 = energy at full height.