====== Energy in Physics ======
Energy is the capacity to do work. This articles explains the relationships between the various forms of energy and work. Energy is represented with the Joule((J)) SI unit which is equal to $\frac{\text{kg} \times m^2}{s^2}$.

===== The Law of Conservation of Energy =====
Similar to the Law of Conservation of Matter, the Law of Conservation of Energy states that Energy cannot be created nor destroyed, but can be converted from one form to another.
  * $\Sigma E = \text{GPE} + \text{KE} + W_f$ where $\Sigma E$ is total energy, $\text{GPE}$ is the gravitational potential energy, $\text{KE}$ is kinetic energy, and $W_f$ is the final work energy((work doesn't have to be in the system for it to count in this equation)).

===== Types =====
There are two types of energy that we care about in physics class, Gravitational Potential Energy((GPE)) and Kinetic Energy((KE)).
==== Gravitational Potential Energy ====
Gravitational Potential Energy is the stored energy of an object and is derived from its position.
  * $\text{GPE} = mgh$ where $m$ is mass((kg)), $g$ is gravity((9.8 m/s^2)), and $h$ is height((meters)).
==== Kinetic Energy ====
Kinetic Energy is the energy associated with an object's motion. It is defined as the work needed to accelerate an object from rest to its final velocity.
  * $\text{KE} = \frac{1}{2}mv^2$, where $\text{KE}$ is kinetic energy, $m$ is mass((kg)), and $v$ is velocity((m/s)).

===== Work =====
Work is the physical movement of an object over a certain distance as a result of a force. Work is represented as a scalar quantity, meaning magnitude or direction is omitted, and uses the same unit as energy, the Joule((J)). As energy is the quantitative measurement of work capacity, it also represents the transfer of energy from one system to another, like from potential to kinetic((aka the difference)).
  * $w = \Delta e$, where $w$ is work and $\Delta e$ is the change in energy.
  * $w = e_f = e_i$, where $w$ is work, $e_f$ is the final energy, and $e_i$ is the initial energy((derived from the above equation)).
  * $w = FD$, where $w$ is work, $F$ is the force((Newtons)), and $D$ is physical displacement((meters))((the fact that work is zero if there is no displacement is intentional)).

===== Power =====
Power is the rate at which work is done. The SI unit of power is the Watt((W)), which is represented as Joules per second((or J/s -> Nm/s -> kg m^2 s^-3)). To convert to shittier units, use Google or remember the conversion yourself idiot. A handout for you: 1 horsepower (hp) is equal to 745.7 watts.
  * $P = \frac{w}{t}$, $w$ is work and is in Joules, and $t$ is time in seconds.
  * $P = FV$((if you think about it, this is actually just a substitution of the work equation $w = FD$ and $V = \frac{\Delta \text{position}}{\Delta \text{time}}$)), where $F$ is force((typically you'll need to substitute it with $F_{\text{net}}=ma$ or $mg$)), and $V$ is the velocity. Velocity needs to be constant for this to work.

===== Elastic Potential Energy =====
Elastic Potential Energy represents the stored energy of a spring. The spring constant((k)) measures the elasticity of a spring, its unit is N/m ((Newtons/meter)).
  * $\text{EPE} = \frac{1}{2}kD^2$ where $k$ is the spring constant and $D$ is the displacement of the spring from rest.