2e: Two Energy Laws

One very important concept in the physics of sound (and for all of physics) is the law of conservation of energy: Energy cannot be created or destroyed but it can be transformed from one type of energy to another.

Consider the following energy conversions. You do 10 J of work on the spring of a toy gun so that 10 J of potential energy are stored. When you pull the trigger the spring energy is converted to 10 J of kinetic energy and a ball leaves the gun going upward. The kinetic energy gradually turns into gravitational potential energy as the ball goes upward. Halfway up it has 5 J of kinetic energy and 5 J of potential. At the top there is no kinetic left but you have 10 J of gravitational potential energy. On the way down the potential energy is gradually converted to kinetic energy. Just before the ball hits the ground it has 10 J of kinetic energy. Once it hits the ground the 10 J is converted to sound and heat; the ball is just a tiny bit warmer than it was.

You can also trace the original 10 J back in time before you pushed the spring on the toy gun. The energy for moving your arm came from chemical energy stored in your body. This chemical energy came from the plants and/or animals you ate. That energy can eventually be traced back to the nuclear energy released in the form of electromagnetic waves from the sun. Plants absorbed this light energy to form stored chemical energy for you to eat. Energy was never created or destroyed in any of these conversion steps. The law of conservation of energy is also called the first law of thermodynamics.

There is a second energy law that is also very important but we will not need to know the details of how it works. The second law of thermodynamics says that anytime you change energy from one form to another, some of the energy must (that is the law!) end up in a much less useful form as random thermal energy (heat). When the mechanical energy of bowing a violin is turned into vibrational energy in the strings and then that energy is turned into sound energy in the air, a small amount of the total energy always ends up as heat. The violin and surrounding air will be just a tiny bit warmer. Likewise, amplifiers for radios, stereos and electric guitars give off heat because they are converting electrical energy into sound energy; according to the second law the conversion process has to give off some heat.

Here are a few Slides on the Second Law to give you an idea of how universal this law is and what its effects are. Notice that some conversion processes are much more efficient than others but they all lose some energy (and they have to because of the second law). Your car motor is very inefficient, losing 75% of the energy as heat. New technology may improve things some but as long as you are burning gasoline the efficiency of a car motor will remain well below 50% because of the second law of thermodynamics.

Video/audio examples:

Energy conservation:

Simulation exercise 2D (turn in answers on a separate sheet of paper): Energy Conservation in a Spring Simulation.
Simulation exercise 2E (turn in answers on a separate sheet of paper): Download and play with the Skate Park Simulation and answer the questions below.
      1. Click on ‘clear heat’, ‘pie chart’ and ‘bar graph’ and run the simulation.
      2. What is the relationship between Kinetic, Potential and Total energy? (Be specific! Use the concept of conservation of energy to explain what you are seeing.)
      3. Describe what happens if you start the skater further up on the track. Why does this occur?
      4. Click on the Track Friction Button and add a little friction. Describe the relationship between the different kinds of energy if there is friction.
      5. Use the concept of conservation of energy to explain what you are seeing.
      6. Add a track, or two, to make a new design. To do this, go to the upper left hand corner and drag the piece of track to connect it to the existing one. Describe your design.
      7. Click on the ‘change skater’ feature. How does the mass of the skater change what you are seeing? What happens when a new skater is on the moon? Be specific in your answers.
      8. Once your adjusted track is set, where is the skater when the potential energy is the highest? Explain.
      9. Where is the skater when the kinetic energy seems to be equal to potential energy? Explain.
Simulation exercise 2F (turn in answers on a separate sheet of paper): Download and play with the Spring Simulation and answer the questions below.
      1. Turn the friction off, set g = 0, hang a 100g weight on the 3rd spring, pull it down and let it go. In the show energy box, click on ‘spring three’. The total energy, the spring potential energy (PEelas), the gravitational energy (PEgrav), the kinetic energy (KE) and the thermal energy (Thermal) are shown. Carefully describe what happens to these different energies as the spring bounces up and down (You may want to slow the simulation down to 1/4 time to see what is going on).
      2. Describe the relationship between the different kinds of energy as the spring potential energy goes down the kinetic energy ____?
      3. In this simulation, what happens if you put a different mass on the spring? Why?
      4. In this simulation, what happens if you change the stiffness of the spring? Why?
      5. Turn friction on and describe the relationship between the different kinds of energy when there is friction.
      6. Turn friction off and gravity on. Describe the relationship between the different kinds of energy for different amounts of gravity.

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