These are prerequisite charts and suggested sequences for study modules of the Calculus-Based Physics Personalized System of Instruction:

I. Mechanics, Sound, Heat

II. Electricity, Magnetism, Light

Each "road map" is linked to the texts of the modules in this repository.

]]>Recommended

1. What is the Philosophy of PSI?

2. How Do I Manage This System?

3. The Care and Feeding of Student Tutors

Optional

4. How to Plan the Content of a Keller Plan Course

5. How to Design a Study Module

6. How to Write Learning Objectives

]]>The physicist distinguishes among several types of energy, including kinetic energy (associated with a flying arrow or other moving object), elastic energy (associated with stretched or compressed strings), chemical energy (associated with fuel-oxygen systems or a storage battery), thermal energy (associated with the sun and other objects that are hotter than their surroundings), and nuclear energy. Applications of the energy concept in the science of mechanics, which you are studying now, usually concentrate on kinetic energy, potential energy (to be introduced in the module **Conservation of Energy**) and work (the transfer of energy by the action of a force. Sometimes the phrase "mechanical energy" is used to refer to the forms of energy of importance in mechanics.

When you get on your bicycle, you have undoubtedly noticed that it takes a good deal of effort to get yourself moving rapidly. If you exert yourself very strenuously, you can reach a given speed after a short distance; or you can take it easy and pedal over a longer distance to reach the same speed. In some sense it always takes the same amount of "work" to reach a given speed -- either a large exertion for a short distance or a small exertion for a long distance. You may also have noticed that if you are carrying a passenger on your bike, then it takes more "work" to reach the same speed.

It turns out that these intuitive relationships among the "work" done on a system, its mass, and changes in its speed can be sharpened into a precise statement, called the work-energy theorem. (One caution, though: the technical definition of work needed for this precise statement is different from its everyday usage and physiologic meanings; e.g., you do no work on a heavy box by merely holding it still.) As you will begin to see in the present module, this relationship between work and mechanical energy gives you a new and powerful tool for the solution of many problems, a tool that is often easier to use than a direct application of Newton's second law.

]]>Several different definitions of vector multiplication have been found useful in physics; in this module you will study two types: the scalar and vector products. Just to sharpen your interest, we point out that the vector product has the strange but useful property that A × B = –B × A !

]]>Although waves on water are the most familiar type of wave, they are also among the most complicated to analyze in terms of underlying physical processes. We shall, therefore, not have very much to say about them. Instead, we shall turn to our old standby -- the stretched string -- about which we have learned a good deal that can now be applied to the present discussion.

]]>This module focuses on the first of two central thermodynamic principles: the conservation of energy, or, as it is sometimes called, the first law of thermodynamics. The second basic principle, which deals with the inevitable increase of a quantity called entropy, is the subject of another module Second Law and Entropy. These two abstract principles, plus a few other concepts and laws and the vocabulary needed for literacy in the field, are the entire content of thermodynamics. The energy and entropy principles form the framework that governs all energy conversions involving heat; they are the touchstones we must rely on as we attempt to create new energy devices, such as solar converters or fusion reactors, to limit the wasteful exploitation of the Earth's resources.

The approach of this module is macroscopic -- that is, we shall deal with systems that are approximately of human scale in size and mass (thermometers, blocks of ice, heat engines), and we shall choose observable quantities such as pressure, volume, and temperature to describe the behavior of these systems. The macroscopic approach should be seen as supplementary to the microscopic approach, which regards the behavior of the atoms and molecules as fundamental. This latter framework chooses the molecular velocities, energies, and momenta as the starting point, and values for macroscopic observables are derived from the microscopic picture. The microscopic approach is treated in another module **Kinetic Theory of Gases**, where the behavior of gases is interpreted in terms of molecular energies and collisions.

In order to deal with sound, we should have some idea of what it is. What factors determine whether a sound is pleasing or grating? How is sound transmitted? How much power do our ear drums actually receive when we hear a bird, or a rock band? What determines whether our ears detect a sound; what is the meaning of sound beyond the range audible to a human? These are just a sample of a multitude of physical and physiological questions that one might ask about sound. Not all of these questions will be answered in this module, but you will learn enough to begin finding answers to several of them.

]]>In this module you will study the special kind of periodic motion that results when the net force acting on a particle, often called the restoring force, is directly proportional to the particle's displacement from its equilibrium position; this is known as simple harmonic motion. Actually, simple harmonic motion is an idealization that applies only when friction, finite size, and other small effects in real physical systems are neglected. But it is a good enough approximation that it ranks in importance with other special kinds of motion (free fall, circular and rotational motion) that you have already studied. Examples of simple harmonic motion include cars without shock absorbers, a child's swing, violin strings, and, more importantly, certain electrical circuits and vibrations of a tuning fork that you may study in later modules.

]]>Well, then, perhaps we should concentrate just on the operation of the heat engine, step 2 above. Present-day gasoline engines convert only a small fraction of the "heat energy" released in their cylinders into useful work. Since we are being pinched by energy shortages, why not gear up a research program to develop engines with (say) 90% efficiency? Again, this too is impossible!

These are illustrations of the fact that energy is often unavailable (or only partially available) for conversion into work. There is a fundamental limit to the efficiency that can be obtained in this conversion -- a limit that cannot be surpassed, regardless of technological developments. The basis of that limit is the subject of this module.

]]>The trigonometric functions are defined with respect to a right triangle as follows:

sin θ = y/r

cos θ = x/r

tan θ = y/x

The values of the trigonometric sine, cosine, and tangent functions for a given θ can be determined from a table such as in the appendix to your text or the last page of this module. You can also get the values by use of most slide rules ("S" and "T" scales) and many electronic calculators.

]]>*y* = A sin(k*x* – ω*t*),

where A, k, and ω are constants, Then, "the partial derivative of *y* with respect to *x*" is denoted by ∂*y*/∂*x* and is found by setting *t* constant and differentiating with respect to *x*:

∂*y*/∂*x* = kA cos(k*x* – ω*t*),

Similarly, "the partial derivative of *y* with respect to *t*" is denoted by ∂*y*/∂*t *and is found by setting *x* constant and differentiating with respect to *t*:

∂*y*/∂*t* = –ωA cos(k*x* – ω*t*).

Note that the value of either of the partial derivatives depends on both independent variables *x* and* t *as well as the constants A, k, and ω.

**Input Differentiation Operation Output**

f(x) → f ' (x) = df/dx

the function f(x) being input to an "analytical machine" that manufactures as output the derivative of f. A detailed mathematical prescription for the differentiation operation is nontrivial. It usually involves a quarter or semester course, which requires time, attention, and effort on the student's part.

]]>At the end of the nineteenth century, Newtonian mechanics and Maxwell's electromagnetic theory seemed to explain all physical phenomena, and some scientists believed that physics as a creative science was finished! Yet there was a serious gap: the ether, the postulated medium necessary for the propagation of electric and magnetic fields, appeared to have several incompatible properties. To resolve the ether problem, Einstein reformulated theoretical physics by introducing an operational approach that made use of light signals propagating at the speed c = 3.00 x 10^{8} m/s relative to all inertial frames. This approach replaced the view that space and time have certain absolute properties, as assumed by Newton and his successors.

Incidentally, the "special" in special theory of relativity refers to the fact that only uniform relative motion is considered. Accelerated reference frames, such as those attached to projectiles, are not treated in the special theory of relativity, but are the subject of Einstein's general theory.

]]>This module treats kinematics, which is the part of physics concerned with the description of the motion of a body. The body may be an automobile, a baseball, a raindrop, a flower in the wind, or a running horse. The change in position of a body can be described in terms of the vector quantities: displacement, velocity, and acceleration. Calculus can be used to define the relationships among these quantities. It is therefore essential to know some basic techniques of calculus to understand the content of this module.

The applications in this module only consider motion in one dimension. A later module will treat the more general case of motion in two or three dimensions, but the fundamental concepts will be essentially the same.

]]>Two important applications that will be utilized many times in later modules are covered here. First is the motion of a particle experiencing constant acceleration, e.g., a baseball in flight. Second is the motion of a particle in a circular path with a constant speed, e.g., an earth satellite in circular orbit.

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