# Physics Commons™

Calculus-Based General Physics

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## Full-Text Articles in Physics

#### 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 ...

Jan 1975

#### 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.

Jan 1975

#### Ampère's Law

##### Calculus-Based General Physics

Everyone has seen a bar magnet in the form of a compass or a door catch. Anyone who has ever casually played with magnets or magnetic toys knows that magnets interact with other magnets; i.e., a magnet experiences a force caused by thp presence of an external magnetic field produced by the other magnet. A wire carrying a current experiences a force caused by the presence of a nearby magnet (as you saw in the module Magnetic Forces). We then expect the converse to also hold true, i.e., that the bar magnet will also experience a force from ...

Jan 1975

#### 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 ...

Jan 1975

#### Capacitors

##### Calculus-Based General Physics

Capacitors are important components of electronic circuits and of electrical machinery and power grids. You can find large oil-insulated capacitors on powerline poles or small ceramic-insulated capacitors in a radio. In each application the capacitor is used to store electrical charge and electrical energy - for example, sometimes for a short time in an alternating-current cycle, sometimes for a long time until the energy is needed, as in a strobe light for a camera. Your body can be a capacitor, storing up enough charge and energy to cause a painful spark when the capacitor discharqes.

Practical capacitors are basically two conducting ...

Jan 1975

#### 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 ...

Jan 1975

#### 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) Ug to the cyclist ...

#### 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 ...

Jan 1975

#### Diffraction

##### Calculus-Based General Physics

Have you ever wondered why you can hear around corners, but cannot see around them? You know that light and sound are waves, and should therefore share the same basic properties. Why then do they seem so different in the property of their "shadows"?

In this module you will learn that light does exhibit all the bending properties of sound and water waves. The effect, however, depends on the size of the obstacle compared to the wavelength. It is only the largeness of everyday obstacles compared to the very small wavelength of light that deemphasizes the bending, or diffraction, of ...

Jan 1975

#### 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 ...

#### 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 understanding ...

Jan 1975

#### 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 ...

Jan 1975

##### 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.

Jan 1975

#### Equilibrium Of Rigid Bodies

##### Calculus-Based General Physics

Most of the objects that one sees are in a state of equilibrium, that is, at rest or in a state of uniform motion. Many man-made structures are designed to achieve and sustain a state of equilibrium, and this, in turn, sets requirements to the materials (their sizes and shapes) that can be used. This module will give you some practice in analyzing the forces that result in equilibrium. From this analysis, if you are given the values of an appropriate set of forces you can find the remaining ones. On the other hand, in designing a stable system you ...

Jan 1975

#### 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 include ...

Jan 1975

#### 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 ...

Jan 1975

#### 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 establishing this ...

Jan 1975

#### 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 ...

Jan 1975

#### Inductance

##### Calculus-Based General Physics

Anyone who has ever grabbed an automobile spark-pluq wire at the wrong place, with the engine running, has an appreciation of the ability of a changinq current in (part of) a coil of wire to induce an emf in the coil. What happens is that the breaker contacts open, suddenly interrupting the current, and causing a sudden large change in the magnetic field through the coil; according to Faraday's law, this results in a (large) induced emf. In general, the production of an emf in a coil by a changing magnetic field due to a current in that same ...

Jan 1975

#### 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 ...

Jan 1975

#### Introduction To Quantum Physics

##### Calculus-Based General Physics

You have probably encountered a system known as an "electric eye," which senses light from an artificial source or the sun. This information is used to open doors, count pedestrian or auto traffic, turn on lights at sunset, read holes in punched card, and for a host of other applications. Most of these devices are based on the photoelectric effect, which is the light-induced emission of electrons from atoms.

The photoelectric effect completely baffled physicists at the time of its discovery. Einstein's explanation of this process, which won the Nobel Prize in 1921, was a major part of the ...

Jan 1975

#### 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 ...

Jan 1975

#### 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 ...

Jan 1975

#### 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.

Jan 1975

#### Maxwell's Predictions

##### Calculus-Based General Physics

With this module, you will reach a milestone in your study of electromagnetic phenomena. From past modules, you now have (at your fingertips, hopefully!) the same basic laws of electromagnetism that Maxwell collected together in the nineteenth century. However, as powerful as these laws were, Maxwell found that there was a basic flaw -- a logical inconsistency -- in the one known as Ampere's law. He was able to deduce (in advance of any direct experimental test) precisely the correction that was needed. With this correction, the addition of what is called the "displacement-current" term to Ampere's law, it follows ...

Jan 1975

#### Newton's Laws

##### Calculus-Based General Physics

When a body is at rest, we know from experience that it will remain at rest unless something is done to change that state. A heavy box on the floor will stay in place unless it is pushed or pulled. We walk without fear beside a massive rock on level ground because we know it won't suddenly move and crush us.

Undoubtedly you have leaned against a chair only to have it move and send you scurrying for your balance. Did you then question the relationship of the interaction between you and the chair to the ensuing motion of ...

Jan 1975

#### 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 ...

Jan 1975

#### 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 ...

Jan 1975

#### 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 ...

Jan 1975

#### 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.