Potential & Kinetic Energy

Potential energy is energy that is being stored. An example of potential energy is a mass held at a certain height. The higher the particle is off of the ground, the higher its potential energy. Refer to equation 1.

(Eq 1)  $U_{1-2}=WΔy$

W = Weight

Δy = suspended height

U1-2 = Potential Energy

A compressed spring also has a stored potential energy. The potential energy gained by compressing or stretching a spring can be seen in equation 2.

(Eq 2)  $U_{1-2}=-\left( \frac{1}{2}ks_2^2-\frac{1}{2}ks_1^2 \right)$

k = spring constant

s2 = Initial spring length

s1 = New spring length

The variable k in equation 2 represents that spring constant, which represent the amount of deflection caused by a certain amount of force. Refer to equation 3.

(Eq 3)  $k=\frac{f}{δ}$

f = force

δ = change in length

Kinetic Energy

Kinetic energy on the other hand represents the amount of energy being expanded through motion. Kinetic energy is normally represented by equation 4.

(Eq 4)  $T=\frac{1}{2}mv^2$

m = Mass

v = velocity

T = Kinetic Energy