This text is meant to accompany class discussions. It is not everything there is to know about energy. It is meant as a prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Law of conservation of energy (for mechanical energies)

The first law of thermodynamics says that all energy is conserved. This is referred to as the law of conservation of energy. This means if you are sitting, at rest, at the top of a playground slide and then slide down to the bottom, all the forms of energy at the top and the bottom of the slide add up to give the same number. It is written like the the line shown below.

If this expression is applied to the slide example above, it would be written as

Since only two forms of energy are being considered, it could further be described as

Energy is exchanged within a system. Here are some components of a system.

Energy form

associated object

kinetic energy

any "body"

gravitational potential energy

the Earth

spring potential energy

springs

thermal energy

air, atmosphere, water

non-conservative energy/force

source of the force

Energy Systems

The system for a boy swinging in a swing on a playground. The system is the boy and the Earth. this is because the boy's kinetic energy is exchanged with the Earth's gravitational potential energy. The system is defined as the body and the Earth because they exchange the energy.

An air-soft gun propels a "soft" projectile via a spring in a pistol as the pistol is pointed upwards. Potential energy stored in the spring is delivered to the projectile's kinetic energy and then to the Earth's gravitational potential energy as the projectile rises in the air. The system is defined as the spring, body, and the Earth because they exchange the energy.

Inside of an airsoft pistol. The spring is on the left. Image by "Elwenil."

A soccer player is running and slides horizontally on the playing field until he comes to a rest. The kinetic energy of the player drops to the ground and then slides until he loses all of his energy to thermal energy by heating up the ground/air. The system is defined at the body, Earth, and the atmosphere.

Example 16

This video shows how to apply the law of conservation of energy to problem solving.

The second law of thermodynamics (when applied to mechanical energies) says all mechanical energies are not conserved but it can be accounted for by the work of nonconservative forces. Mathematically it looks like this

Where the work is work by nonconservative forces. Conservative forces, such as gravity, springs and other elastic forces, have their own formula for calculating the energy and do not need to be described by these works. Other forces, such as those from motors, rockets, frictions, air resistance, etcetera, are non conservative forces. When work is done by a nonconservative force, energy is either added to subtracted from the body. the energy is accounted for through work.

Example 17

Earlier you calculated work using the formula "Fd", when given a graph of force vs displacement, work is the area between the curve and the zero axis. When calculating the net work, you add up all the areas for the given displacement while keeping in mind that the areas above the axis are positive and areas below the axis are negative.

Energy Flow Diagrams

An energy flow diagram is a simple bar graph that, describe
s the relative amounts of energy at any location. Through this unit on energy you have seen bar graphs showing different amounts of the forms of energy. If you combine all these bars onto a graph and then create different graphs for each location, then the the collection of graphs are called energy flow diagrams. These diagrams reflect the forms of energy and the law of conservation of energy. The specific length of the bars is not important. What is looked for are the trends in the bars. For example, a car is slowing down and successive energy bar graphs are drawn. As the car slows down the kinetic energy bars also decrease while the energy goes somewhere else. In this car slowing down example, the energy goes into thermal energy.

Below is an example of a collection of energy flow diagrams showing what happens to the rider's forms of energy.

As the snowman travels down the hill he picks up speed. Speed is related to kinetic energy. At the bottom, his kinetic energy, (KE), bar gets bigger. Because he is lower than he started at the bottom of the hill, his potential energy (PE) decreases. That is why that bar is closer to zero. After reaching the bottom the snowman leaves the snow and slides against the ground. The ground slows him down. He loses speed without changing height. The energy goes into thermal energy. It is lost from the system of the sled and hill.

What do you think the energy flow diagram for the animation and the three locations will look like?

Energy flow diagrams can help you understand how energy is transferred from energy form to energy form. The diagrams can be transfered to the math model showing the law of conservation of energy. The diagrams also provide an easy way to conceptually discuss what is happening.

Example 13

Example 14

Example 15

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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