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 Joule¹⁾ SI unit which is equal to $\frac{\text{kg} \times m^2}{s^2}$.

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 energy²⁾.

There are two types of energy that we care about in physics class, Gravitational Potential Energy³⁾ and Kinetic Energy⁴⁾.

Gravitational Potential Energy is the stored energy of an object and is derived from its position.

• $\text{GPE} = mgh$ where $m$ is mass⁵⁾, $g$ is gravity⁶⁾, and $h$ is height⁷⁾.

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 mass⁸⁾, and $v$ is velocity⁹⁾.

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 Joule¹⁰⁾. 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 kinetic¹¹⁾.

• $w = \Delta e$, 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 energy¹²⁾.
• $w = FD$, where $w$ is work, $F$ is the force¹³⁾, and $D$ is physical displacement¹⁴⁾¹⁵⁾.

Power is the rate at which work is done. The SI unit of power is the Watt¹⁶⁾, which is represented as Joules per second¹⁷⁾. 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.
• $P = FV$¹⁸⁾, where $F$ is force¹⁹⁾, and $V$ is the velocity. Velocity needs to be constant for this to work.

Elastic Potential Energy represents the stored energy of a spring. The spring constant²⁰⁾ measures the elasticity of a spring, its unit is N/m ²¹⁾.

• $\text{EPE} = \frac{1}{2}kD^2$ where $k$ is the spring constant and $D$ is the displacement of the spring from rest.