Conservation of Mechanical Energy

Potential energy

The potential energy of an object is the energy stored in an object or system. Denoted as Ep.
Generally speaking, potential energy refers to potential energy caused by gravity and is proportional to the mass and height of an object.
When a spring is deformed by external force, it has energy also, which is called ‘potential energy by elastic force’.

\[ \begin{align} Potential\;energy\;caused\;by\;gravity\;E_p &= 9.8 m h \\ Potential\;energy\;by\;elastic\;force\;E_p &= \frac{1}{2}mx^2 \end{align} \]

m: mass(kg)
h: Height(m)
k: spring constant(N/m)
x: deformation length of spring(m)

Kinetic energy

Kinetic energy is the energy in a moving object or particle. Denoted as Ek.
Since the kinetic energy at rest is ‘0’, the kinetic energy becomes the energy required to accelerate an object of mass m to speed v.

\[ Kinetic\;energy\;E_k = \frac{1}{2}mv^2 \]

m: maxx(kg)
v: velocity(m/s)

Energy conversion

One energy can be converted to another. If there are no losses due to friction, the energy can be converted to 100% other energy.
The lost energy escapes with the form of heat.