1. Montero1
Lorenzo Montero
Mr. Rice
Physics B 420
Spring Semester Thesis
Our universe is a dark, spooky, mysterious place. Everything in this universe is set in
motion—down to the quantum level—due to the "Big Bang". There's an irony in this universe,
and that is all forms of energy is conserved, even though our universe was sparked by a
euphemism, "The Big Bang". Mechanical energy is conserved, meaning that Mechanical energy
input = Mechanical energy output. Collisions and transfer of momentum also have conservation
of energy. In addition, thermal energy is also conserved. Furthermore, the energy in vibrations
and waves conserve energy. Lastly, electrical energy is conserved as well. So, how do these
quintessential laws of physics all relate to the conservation of energy?
To elaborate on this, mechanical energy is conserved. KEi + PEgrav,i + PEelastic,i +
PEelectric,i = KEf + PEgrav,f + PEelastic,f + PEelectric,f. In other words, Initial Kinetic Energy + Initial
Gravitational Potential Energy + Initial Elastic Potential Energy + Initial Electric Potential
Energy = Final Kinetic Energy + Final Gravitational Potential Energy + Final Elastic Potential
Energy + Final Electric Potential Energy. To encapsulate this, Initial Mechanical Energy = Final
Mechanical Energy. Objects in motion have kinetic energy [(
1
2
)(m)(V2)] because of their mass
and speed. Potential energy is energy associated with an object's position. Three forms of
potential energy are gravitational potential energy [(m)(g)(h)], elastic potential energy
[(
1
2
)(k)(X2)], and electrical potential energy [-(q)(E)(d)].

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Believe it or not, energy is still conserved even if you’re involved in a collision, whether
if it’s from a car crash or if you get tackled in football. A car crash is an example of an elastic
collision. If there is a Lamborghini at a red light and a monster truck slams the rear end of the
Lamborghini, then the Lamborghini will be launched to the other side of the intersection.
However, the truck will come to a complete stop. Momentum is defined as mass times velocity
[in (kg)(
𝑚
𝑠
)]. In the car crash scenario, the monster truck will transfer its momentum to the
Lamborghini. Since the Lambo is at a stop light, it’s momentum is zero (it has mass, but no
velocity). Initial: Truck Lambo (Stationary)
Final: Truck (Stationary) Lambo As you can see, momentum is
conserved during the whole process. (m1,i)(V1,i) + (m2,i)(V2,i) = . (m1,f)(V1,f) + (m2,f)(V2,f).
Another type of collision is inelastic collision, such as a football player tackling a wide receiver.
This collision is inelastic, because the tackler “sticks” with the wide receiver, resulting in a
combined mass of the two. The equation for inelastic collision is: (m1,i)(V1,i) + (m2,i)(V2,i) =
(m1 + m2)(Vf). So where did the energy go? It didn’t just disappear when the linebacker tackles
the wide receiver. Some of the energy was converted into internal energy. In an elastic collision,
two objects stick together and move as one mass after a collision. Kinetic energy [(
1
2
)(m)(V2)] is
converted to internal elastic potential energy when the objects deform. Some kinetic energy is
also converted to sound energy and internal energy. If the law of calculus is applied, momentum
is the derivative of kinetic energy, likewise, kinetic energy is the anti-derivative or integral of
momentum. Back to the football players, momentum is conserved but kinetic energy is not
conserved in an elastic collision. Altogether, in all interactions (elastic or inelastic collisions)
between isolated objects, momentum is conserved.

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Another form of energy that is conserved is thermal energy. Heat is a misconception
among the masses, because heat is a sensed by our nerves and is sent to our brain telling us that
it’s hot. In physics, heat is energy that is transferred from objects at higher temperatures to
objects at lower temperatures. By definition, temperature is a measure of the average kinetic
energy of the particles in a substance. A cup of boiling water is at a high temperature, because
each individual water molecule is moving at such a high kinetic energy. In contrast, water at
room temperature is cooler, because water molecules are moving at a much slower rate. Energy
is transferred by thermal conduction through particle collisions. Furthermore, heat energy is
conserved when mechanical energy and internal energy are taken into account.
A fourth form of energy that is conserved is in vibrations and waves. In waves, people
think that if an object is on a wave, it will travel along the wave’s motion. However, the object
will just move up and down. You can see this as birds sit on a ocean wave while remaining on
the same spot for a long period of time. As a wave travels, the particles of the medium (meaning
the air, ocean, etc.) vibrate around an equilibrium position. “When a pebble is dropped into a
pond, the water wave that is produced carries a certain amount of energy. As the wave spreads to
other parts of the pond, the energy likewise moves across the pond. Thus, the wave transfers
energy from one place in the pond to another while the water remains in essentially the same
place. In other words, waves transfer energy by the vibration of matter rather than by the transfer
of matter itself. For this reason, waves are often able to transport energy efficiently.” (Book)
Lastly, electrical energy was yet another form of energy that is mysteriously conserved.
The concept of electricity baffled scientists in the 17th and 18th centuries. Electrical potential
energy is energy that a charged object has because of its shape and its position in an electric

4. Montero4
field. Electrical potential energy is the product of charge, electric field strength, and
displacement from the reference point in the direction of the field. PEelectric = -(q)(E)(d)
Units: Joules = -(Coulomb)(Electric Field Strength [
𝑁𝑒𝑤𝑡𝑜𝑛𝑠
𝐶𝑜𝑢𝑙𝑜𝑚𝑏
])(Displacement). Strangely enough,
the units electric potential energy simplify into word (Work = Force * Displacement). Electric
potential energy eerily coincides with the concept of gravitational potential energy
[PEgrav=(mass)(gravity)(height)].