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 $\frac{\text{kg} \times m^2}{s^2}$.

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 energy2).

Types

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

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 mass5), $g$ is gravity6), and $h$ is height7).

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 mass8), and $v$ is velocity9).

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 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

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

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.
1) , 10)
J
2)
work doesn't have to be in the system for it to count in this equation
3)
GPE
4)
KE
5) , 8)
kg
6)
9.8 m/s^2
7) , 14)
meters
9)
m/s
11)
aka the difference
12)
derived from the above equation
13)
Newtons
15)
the fact that work is zero if there is no displacement is intentional
16)
W
17)
or J/s → Nm/s → kg m^2 s^-3
18)
if you think about it, this is actually just a substitution of the work equation $w = FD$ and $V = \frac{\Delta \text{position}}{\Delta \text{time}}$
19)
typically you'll need to substitute it with $F_{\text{net}}=ma$ or $mg$
20)
k
21)
Newtons/meter

Navigation

bruh

QR Code
QR Code physics:energy (generated for current page)