Other Physics Commons^™

Kinetic Theory Of Gases

Calculus-Based General Physics

As you read this sentence you will experimentally demonstrate the general gas law at least once by breathing in and out. As you expand the volume in your lungs, the pressure drops and air comes in; as you decrease the lung volume the pressure rises and air goes out. Pressure (p) and volume (V) are related; at constant temperature, pV = const.

This relation, called Boyle's law, was well established before the atomic theory of matter was accepted. In this module you will learn how to apply much of your knowledge of Newton's laws, kinetic energy, momentum, and elastic collisions …

Electric Fields And Potentials From Continuous Charge Distributions

Calculus-Based General Physics

Too bad! In case you have not realized it, not all charges come packaged as points, spheres, infinite cylinders, or infinite planes. Ah, if only it were so: Life would be much easier from a calculational viewpoint, although somewhat limited in geometrical options. But then, mechanics would be simpler if only constant accelerations were observed in nature ... Not to mention centers of mass; moments of inertia, etc.; all would be considerably simpler to calculate in that wonderful world of point masses, constant accelerations, massless strings, and frictionless boards.

Once again calculus is needed to assist us in analyzing and …

Coulomb's Law And The Electric Field

Calculus-Based General Physics

This module beqins the study of electricity. Not only is it true that we see nature's gigantic electrical show in thunderstorm displays with lightning, but the very functioning of our smallest cells depends on the balance of electrically charged ions, and their movement through cell membranes. On a larger scale than cell membranes, water-purification studies with large membranes show promise of "electrically" removing undesired ions or debris from water. The electronic air cleaner is yet another direct application of the material to come: a 7000-V potential difference between a thin wire and flat collecting plates ionizes the air, and the …

Vector Multiplication

Calculus-Based General Physics

How much is A times B? This is a simple question to answer when A and B represent scalars; however, when A and B represent vectors, the answer is not obvious. In fact, on the face of it, one cannot even say whether the result should be a scalar or a vector!

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 = …

Fluid Mechanics

Calculus-Based General Physics

An invigorating shower in the morning is usually a pleasant experience except for the pesky shower curtain slapping your legs and allowing water to run on the floor. You would think that the downward stream of water would be enough to keep the curtain back even without water striking the curtain. But not so: fast-moving fluids (water spray causing a downdraft of air) contain a low-pressure region. Thus the pressure outside the shower is greater than the pressure inside - with the result that the curtain is blown in and flops against your legs.

More technical applications of fluid mechanics …

Planar Motion

Calculus-Based General Physics

Enough of this physics where things move along straight lines only! We know that most interesting real-life motions involve curves of many and varied shapes. This module extends your understanding of kinematics from one dimension to two dimensions. To accomplish this, you will combine your knowledge of calculus and vectors with concepts like position, displacement, velocity, speed, and acceleration.

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 …

Lenses And Mirrors

Calculus-Based General Physics

If you have ever worn glasses, used a magnifying glass, looked through a telescope, or looked in a mirror, you have some idea of the effect that transmitting and reflecting materials have on light. When light passes from one material to another it is refracted. It is this property of light that is used in making eye glasses and magnifying glasses. The laws of reflection and refraction have immediate application in the construction of optical instruments. Two main objectives of most optical devices are to increase the light-gathering area and to provide a magnified image. Magnification is not usually the …

Collisions

Calculus-Based General Physics

If you have ever watched or played pool, football, baseball, soccer, hockey, or been involved in an automobile accident you have some idea about the results of a collision. We are interested in studying collisions for a variety of reasons. For example, you can determine the speed of a bullet by making use of the physics of the collision process. You can also estimate the speed of an automobile before the accident by knowing the physics of the collision process and a few other physical principles. Physicists use collisions to determine the properties of atomic and subatomic particles. Essentially, a …

Flux And Gauss' Law

Calculus-Based General Physics

Charles Augustine de Coulomb (1736-1806) designed his famous experiment to measure the force relationships between charged bodies: Coulomb's law is the resulting empirical statement. Gauss' law (Karl Friedrich Gauss, 1777-1855), which you will learn in this module, has a more obscure origin. It was originally a mathematical theorem. Scientists in Gauss' nineteenth century were much more inclined than we are today to equate mathematical correctness with physical correctness. When it was realized that Gauss' (mathematical) theorem could be applied to the electric-field concepts of Faraday to produce Gauss' (physical) law, this extension was eagerly accepted. The origins of the law, …

Optical Instruments

Calculus-Based General Physics

You are now familiar with some of the properties of idealized single lenses and simple spherical and plane mirrors. Almost all optical instruments are made up of a combination of lenses, some close together and others far apart. Real lenses and mirrors have many undesirable properties intimately interconnected with their desirable properties. By making careful and clever combinations of lenses one can enhance the desirable and minimize the undesirable characteristics. In this module you will begin the study of some simple combinations of mirrors and simple lenses; it will give you some insight into the complications and fascinating possibilities of …

Relativity

Calculus-Based General Physics

Seldom has a development in science captured the attention of the general populace to the extent that Einstein's special theory of relativity did. Once, after giving a public lecture, Einstein was on the way to the railroad depot when he was asked to summarize his theory in one sentence, in a way the general public could understand. His reply: "When does the station get to the train?" Many of the predictions of the theory violate common sense -- lengths change, times change, masses change, depending on who is looking -- but the theory has been proved correct whenever it has …

Rectilinear Motion

Calculus-Based General Physics

How long does it take you to go home? This depends on how far you are from home (displacement), how fast (velocity) you can travel, and how often you must start and stop (acceleration).

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 …

Direct-Current Circuits

Calculus-Based General Physics

One way to help you understand a new phenomenon is to show you that it is like something that you are already familiar with. This method is used very frequently in physics, e.g., the electric field is like the gravitational field. This module will introduce you to a simple class of RC circuits in which there are currents, charges, and voltages that decay exponentially. This may be your first detailed study of exponential decay, but it is like (analagous to) radioactive decay, Newton's law of cooling, the final depletion of a natural resource, the decrease in atmospheric pressure with altitude, …

Electric Potential

Calculus-Based General Physics

You have no doubt noticed that TV sets, light bulbs, and other electric appliances operate on 115 V, but electric ovens and clothes dryers usually need 220 V. Batteries may be rated at a harmless 1.5, 6, 9, or 12 V, but a high-tension electric transmission line may provide electric power at 400,000 V. Now just what physical quantity is measured by all these volts? How do volts relate to force, energy, and power, about which you have learned in earlier modules? The answer is that volts measure electric potential difference (sometimes called "voltage"), which is derived from the potential …

Interference

Calculus-Based General Physics

You may have observed the sound from your radio fade in and out as you listened to some distant station. Or perhaps you have sat in a "dead" seat in a poorly designed concert hall where, despite the fact that no physical object is between you and the performer, the sound is distorted and weak. Perhaps you have held two fingers close together and looked with one eye through the narrow slit separating the fingers and observed those mysterious black lines in and parallel to the slit. These and many other similar phenomena result from the interference of two or …

Magnetic Forces

Calculus-Based General Physics

It may surprise you to learn that the conversion of electrical energy to mechanical work in electric motors or stereo loud speakers is seldom done by electrostatic forces (Coulomb's law). Magnetic forces associated with moving charges (currents) are the basis of most electromechanical devices. In analogy with the electrostatic case, we introduce an intermediary called the magnetic field. This module considers the forces on currents or moving charges in a magnetic field; the module Ampere's Law will show how magnetic fields are generated by currents.

Rotational Motion

Calculus-Based General Physics

There is a motion of a system of masses that is as simple as the motion of a point mass on a straight line. It is the rotation of a rigid body about a fixed axis. For example, we live on a rotating earth, use rotating devices such as a potter's wheel or a phonograph turntable, and test our luck with a spinning roulette wheel. All of these are objects whose motion is described by the time dependence of a single variable, the angle of rotation. We shall study the angular equivalent of uniformly accelerated motion for some rotating objects. …

Applications Of Newton's Laws

Calculus-Based General Physics

Perhaps at some time you have had occasion to swing a massive object at the end of a rope. Maybe you have watched a parent swing a child around by his outstretched arms or have been fortunate enough to watch an athlete throw the hammer. But all of you have heard or watched an automatic washer go through a spin-dry cycle. How was this spinning drum with holes in its periphery able to speed up the "drying" process? The clothes were too large to pass through the holes in the drum and were "held" in a circular path but the …

Simple Harmonic Motion

Calculus-Based General Physics

Have you ever felt you were the slave of a clock? Clocks are mechanisims that include a pendulum or balance wheel whose repeated patterns of movement define equal time intervals, one after another. Such repeated movements are called periodic motion. Periodic motion may occur when a particle or body is confined to a limited region of space by the forces acting on it and does not have sufficient energy to escape.

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 …

Second Law And Entropy

Calculus-Based General Physics

Suppose you get into your car and drive to _________.* During this trip, (1) the burning of the gasoline in the engine cylinders converts chemical energy into thermal energy of the gases -- that is, they become very hot; (2) the expansion of these hot gases turns the crankshaft, performing work; and (3) this work, transmitted to the wheels, gives the car kinetic energy -- which must be continually replenished, because of depletion by friction and air resistance. At the end of this trip, ____ gallons of gasoline have been converted into water vapor, carbon dioxide, and sundry less desirable …

Faraday's Law

Calculus-Based General Physics

Consider the electric light you may be using to read this module by and the influence on your life style of the vast amounts of electrical energy produced in the United States. This module treats the fundamental principle that allows for the transformation of mechanical energy into electrical energy. The physical law that governs the production of electric current is named after its discoverer, Michael Faraday.

Ohm's Law

Calculus-Based General Physics

Recently you have heard many ways of reducing energy consumption in the home. One of the suggested ways is to use 60-W liqht bulbs rather than 100-W bulbs; another is to cut back on the use of electrical appliances. You readily identify these suggestions with decreasing the amount of "electricity" beinq transported through the wires coming into your home.

You were warned quite early in life not to stick a metal knife into the toaster to force out burning bread; you either unplug the toaster or use a utensil with a wooden handle. Why? Because you were warned of the …

Rotational Dynamics

Calculus-Based General Physics

A diver, in making several turns in the air, grabs his knees to achieve a high rate of rotation, and a skater does much the same thing when she goes into a spin with arms and legs extended but brings them in close to her body for the extremely rapid part of this motion. This module considers the physics describing these motions, and those of other rotational systems -- starting or stopping a record turntable (or a washing-machine tub), unwinding of winch cord as a bucket is dropped into a well, etc.

Traveling Waves

Calculus-Based General Physics

"For many people -- perhaps for most -- the word "wave" conjures up a picture of an ocean, with the rollers sweeping onto the beach from the open sea. If you have stood and watched this phenomenon, you may have felt that for all its grandeur it contains an element of anticlimax. You see the crests racing in, you get a sense of the massive assault by the water on the land -- and indeed the waves can do great damage, which means that they are carriers of energy -- but yet when it is all over, when the wave …

Conservation Of Energy

Calculus-Based General Physics

Imagine a bicycle rider coasting without pedaling along a road that is very smooth but has a lot of small hills. As he coasts up a hill, the force of gravity will, of course, slow him down; but it speeds him up again as he goes down the other side. We say that gravity is a conservative force because it gives back as much kinetic energy (KE) to the cyclist when he returns to a lower level, as it took away when he ascended to the top. We therefore assign a gravitational potential energy (PE) U_g to the cyclist, …

Temperature, Heat, And Thermodynamics: First Law

Calculus-Based General Physics

How can we keep track of energy as it is transferred from one system to another? How can we calculate the amount of internal energy -- a quantity that seems to be hidden within the very "guts" of matter? Further, what is the difference between temperature and heat, and between heat and work?

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 …

Alternating-Current Circuits

Calculus-Based General Physics

The electric clock on the wall, radio and television, the incredibly rapid handling
of information by computers, and the transmission of signals by our own nerves
are among countless devices and effects that depend on circuits in which currents
or voltages vary with time. Alternatinq-current (ac) circuits, in which charges
oscillate back and forth in a wire in such a way that the average current is
zero,are among the simpler time-varying circuits. In this module you will study
the behavior of simple ac circuits containing resistors, inductors, and capacitors.

0 Introduction To Study Modules For Calculus-Based General Physics

Calculus-Based General Physics

These modules were prepared by fifteen college physics professors for use in self-paced, mastery-oriented, student-tutored. calculus-based general physics courses. This style of teaching offers student's a personalized system of instruction (PSI), in which they increase their knowledge of physics and experience a positive learning environment. We hope our efforts in preparing these modules will enable you to try and enjoy teaching physics using PSI.

This is the second printing of the CBP modules. We have tried to remove all of the errors from this material. No doubt, we missed a few, please write to us and tell us any that …

Gravitation

Calculus-Based General Physics

The members of the solar system -- the Sun, the Moon, and the planets -- have held a strong fascination for mankind since prehistoric times. The motions of these heavenly bodies were thought to have important specific influences on persons' lives -- a belief that is reflected even today in horoscopes and astrological publications. A revolution in man's thinking that occurred about four hundred years ago established the concept of a solar system with planets orbiting about the Sun and moons orbiting about some of the planets. Copernicus, Kepler, Galileo, and Newton were the four scientific leaders chiefly responsible for …

Impulse And Momentum

Calculus-Based General Physics

You have already learned that you stub your toe harder trying to kick larger masses. Now imagine another unpleasant activity: catching a bowling ball. This gets harder to do as the ball is dropped from higher places. The difficulty depends both on the ball's mass and its velocity just before you apply the stopping force. This force can be applied in different ways. Any winner of an egg-throwing contest will tell you the way to stop an object with the least force is to spread the stopping process out over a maximum time.

This module will develop the above "folk …