Dynamic Energy in Physics

Energy and Conservation in Physics

By Heidi Hileman

Motion: Galileo Galilei

Galileo, in 1590, wrote a treatise on motion that disputed nearly every assumption made by Aristotelian physics. He stated that bodies composed of the same material fall with the same speed through a given medium regardless of weights using arguments based on the principle of Archimedes. Galileo supposedly said that if you dropped two balls of similar material but different weights off the Leaning Tower of Pisa, they would hit the ground at the same time. Galileo introduced the law of the level, claimed that besides Aristotle's division of all motions into natural and forced, there were also neutral motions exemplified by rotating spheres and motions along horizontal planes.

In 1632, Galileo published Dialogue, reconciling the earth's motion based on Kepler's proof of the solar system as heliocentric with planets revolving around the sun, with man's experience in everyday life with a stationary earth; with the concept of the relativity of motion, the idea of inertia, the law of uniform acceleration and its application to falling bodies, calling for a unified science of physics and astronomy.

Force: Isaac Newton

Based on Galileo's work, Isaac Newton, beginning in 1687 introduced his laws of motion and universal law of gravity in Principia. The first law of motion is that bodies in motion stay in motion and bodies at rest stay at rest, unless acted upon by a force. The second law presents his famous equation:

Force = ma

where m equals mass and a equals the acceleration. Newton's third law presents conservation of momentum, the product of mass and velocity. Since gravity is a natural force that is either slowing motion or speeding it up, Newton introduced his universal law of gravitational force.

Vis Viva: Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz began publishing papers in calculus in 1684 and first introduced the integral. Leibniz introduced the concept of vis viva (living force) which attempted to quantify life force. It is similar to Newton's conservation of momentum, but velocity is squared. Mathematically vis viva was expressed as:

Vis Viva = mv²

There is a definite relationship between size and velocity. The power of a bullet to pierce with its small mass but fast velocity has a lot of vis viva, as does an elephant whose mass is enough to make the ground tremble even at slow speeds. A leaf which is both small and slow has little vis viva, but leaves falling in mass as they do in Autumn have vis viva. (Guillen 1995)

Kinetic Energy

Eventually vis viva was replaced by kinetic energy, the energy of motion, with a proportionality constant of ½ expressed as:

Kinetic Energy = ½mv²

where the ½v² accounts for friction becoming a velocity triangle such as the kind that a rock makes skipping through the water. The derivative of kinetic energy becomes mass times acceleration which works in harmony with Newton's force of F = ma. Newton's force can be integrated to become kinetic energy. Note vis viva can not be derived from Newton's force. Other types of energies were derived such as work (mechanical), thermal, electrical, solar and so on.

Today, however, kinetics is also associated with kinetic theories based on the observation that minute particles of a substance are in vigorous motion due to temperature.

Conservation: Johann and Daniel Bernoulli

Daniel Bernoulli (1700-1782) received his doctorate in medicine. As a professor he taught anatomy, mathematics and physics. Bernoulli chief work was his book Hydrodynamica published in 1738. Bernoulli was fascinated with the flow of blood through the veins. He eventually realized that when the heart pumped blood, the pressure in the veins increases and the velocity of the blood flow decreased. Inversely when the heart relaxes, blood pressure decreases so the speed of the blood flow increases.

Daniel's father, Johann (1667-1748), was also a professor of mathematics and a personal friend of Leibniz and part of a group promoting a Law of Conservation of Vis Viva:

Vis Viva + Altitude = Constant

which was eventually changed to a conservation of energy law more line with Newton's force

Kinetic Energy + Potential Energy = Constant

Here the kinetic energy is the energy applied to say a ball to toss it in the air. The potential energy is the initial position of the ball. The higher the initial position of the ball, the less kinetic energy needed to reach a specified height. Drop the ball, it losses potential until it rests upon the ground and returns to the beginning point.

Daniel changed mass to density and altitude to pressure to create:

Vis Viva + Pressure = Constant

Vis Viva = dv²

which was eventually changed to:

½dv² + Pressure = Constant

and was grouped under conservation of energy. The Bernoulli effect also describes the reason airplanes and jets fly. The top part of the wing is curved with a flat underside. Air is forced to move faster over the top of the wing, reducing pressure, to create lift. (Guillen, 1995)

Conservation of Energy: Rudolf Clausius

Rudolf Clausius in 1850 gathered together the current body of energy equations under a general law he called the Law of Energy Conservation. He said there are many types of energies such as solar, thermal, electrical, work (mechanical), potential, kinetic, and so on. These energies can interchange back and forth into each other, but the sum total of all the energies in the heavens never changes.

Special Theory of Relativity: Albert Einstein

Though vis viva was forgotten for a time in favor of energies that could be integrated with Newton's force, it would resurface in the work of Albert Einstein. Einstein and his wife Mileva Maritsch recognized the mathematical importance of the speed of light as a constant and used it to express the relationship between energy and mass in the Specific Theory of Relativity (1905) by changing v² in the original vis viva equation to c², where c is the speed of light traveling through the vacuum of space:

Energy = mc²

This equation expresses the ability of light to move back and forth between a wave and a particle and is used in quantum mechanics through measurements made by particle accelerators that enable conversion of small subatomic masses into an energy equilivent where all external reactions are kept to a minimum so as to approach the effects of a vacuum (Hawkins 1988). Results are showing an expected increase of mass at high speed. A conceptual reason for this may be electrically charged particles induces a magnetic field that could increase density. The proportionality constant equals 1, because there is little resistance in space and the speed of light is at its maximum. Since the universe is in a state of expansion, gravity acts as a break to degrade and slow light. Einstein developed theories of gravity in his General Theory of Relativity where gravity bends light. Einstein's general theory of gravity allows a more accurate prediction of the orbit of Mercury which is closer to a gravity source, but Newton's and Einstein's theories of gravity are equally effective for planets farther away from the sun such a Pluto.

© 1999 Heidi Hileman
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