Scope, Sequence, and Coordination

A Framework for High School Science Education

Based on the National Science Education Standards


Qualitative Examples of Conservation of Mechanical Energy

Work, Kinetic Energy, Potential Energy, Field Energy, and the Conservation of Energy
WORK AND KINETIC, POTENTIAL, AND FIELD ENERGIES

NSES Generalizations (p. 180)

The total energy of the universe is constant. Energy can be transferred by collisions in chemical or nuclear reactions, by light waves and other radiations, and in many other ways. However, it can never be created or destroyed. As these transfers occur, the matter involved becomes steadily less ordered.

All energy can be considered either kinetic energy, which is the energy of motion; potential energy, which depends on relative position; or energy contained by a field, such as electromagnetic waves.


Further Description:

Here work and kinetic and potential energies are considered in their different mechanical forms. Electrical energy must also be considered, and the concept of "voltage" (i.e., potential energy per unit charge) must be developed. At this point the only thing we need to do in regard to energy dissipation is to note that mechanical systems that are exchanging energy between kinetic and potential "run down." Since mass is also energy and mass energy does not conform to energy as described in the NSES standard, this topic needs to be developed more carefully.

The important connection between a net constant force doing work on an object and thereby increasing the velocity of the object to produce kinetic energy can be established (i.e., F = ma, and W = FD = maD. Since vf2 = 2aD, leading to aD = vf2/2, we have W = mvf2/2, which we define as kinetic energy). Using integral calculus, one can show that the force need not be constant and that the increase in kinetic energy as a consequence of a net force acting through some distance is exactly the increase in kinetic energy (this is called the work-energy relationship).


Concepts Needed:

Grade 9:

Work, gravitational potential energy, kinetic energy

Grade 10

Simple machine, efficiency, conservation

Grade 11

Potential well, translational and rotational kinetic energy

Grade 12

Electric potential energy (and electric potential and potential difference), volt, electron volt, thermal energy, conservative force, nonconservative force, mass-energy equivalence


Empirical Laws or Observed Relationships:
:

In many systems, there is an interchange between kinetic and potential energies, with the total mechanical energy slowly being reduced and with an attendant increase in thermal energy of the system and its surroundings. Examples include the simple pendulum, a ball rolling back and forth in a gravitational potential well, etc.


Theories or Models:

Law of conservation of mechanical energy; E = mc2, theory of special relativity


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Micro-Unit Description:

Qualitative Examples of Conservation of Mechanical Energy
Simple machines should be understood in the context of work input equaling work output as one of the simplest applications of the law of conservation of mechanical energy. Students should then be able to solve problems involving kinetic and potential energies of simple systems and to use the law of conservation of mechanical energy to examine transformations between kinetic and potential energies for systems like a pendulum, a compressed spring, a roller coaster, or a planet in an elliptical orbit around a star.Students should begin to see energy as an accounting system and should be able to describe exchanges of mechanical energy qualitatively in "Rube Goldberg" type devices. (b) The mechanical equivalent of heat should be determined, allowing students to make the connection between calories and joules, and more importantly, between work and heat.


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