Classical Mechanics Unit CM1 Work and Energy

Overview: This unit is the first in a series on classical mechanics. It covers work and energy, which have the same units as must be true if the work-energy theorem is to be valid. It also discusses conservative forces, the definitions of kinetic and potential energy, and the conservation of energy.

D. Kleppner and R. Kolenkow, An Introduction to Mechanics (K&K) Chapt. 4 - Work and Energy; consult Chapt. 1 for a review of vectors, elementary vector calculus, and other mathematical topics.

Comment: K&K is well-written and abounds with instructive and appropriate examples. The problems at the ends of the chapters are in many cases quite difficult, however, an the assigned problems have been chosen with care. The solutions are on file: just ask an instructor if you wish to see them.

Videotape: There is a videotape of a lecture by Prof. Mohan Kalelkar providing an explanation of the key concepts and problem-solving techniques for this unit. If you wish to view the tape during class, ask your instructor to set you up in the nearby video room. This tape can also be viewed in the Math and Science Learning Center (MSLC) by asking at the reception desk for Physics 323 Tape CM1 on Work and Energy.

The video may also be viewed online here

After completing this unit you should understand:

1. It is assumed you are familiar with such basic concepts in mechanics as position, velocity, acceleration, force, momentum, and energy. If you need to refresh your memory you can refer to the earlier chapters of K&K.
2. The definition of work as an (in general path dependent) line integral of the force: W = ∫ F⋅ dr .
3. When the work is independent of the path, or equivalently the work done by the force over a closed path is zero, the force is called conservative. In this case a potential energy function of position can be defined and the total energy, kinetic plus potential, is conserved (constant).
4. The total momentum of a system in any particular direction is conserved when the total external force on the system in that direction acting on the system is zero. (Note that internal forces of different components of the system on one another do not have to vanish.) Only if the total external force in all directions vanishes do we say that momentum is conserved.
5. A system near a local minimum of the potential behaves as a harmonic oscillator.

Problems:

Chapt. 4: Problems 1-4,6,10,13,15,16,25