physics
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Mechanics - Fundamental Quantities
Objectives:
- identify properties of matter and energy and describe the interactions between them
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describe energy/matter and their various forms and relationships
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describe interactions of two or more things and the effect each has on the other
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understand cause and effect relationships that allow predictions to be made
Directions: Read the lesson and complete the Review.
Introduction
The mechanics used in the study of Physics is important to a thorough understanding of the subject matter. In this lesson module, you will learn the fundamental quantities used in Physics.
What are the fundamental quantities generally used in Physics? Explain each one.
Vocabulary
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piezoelectric
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synchronous
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pendulum
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sidereal
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ecliptic
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ambiguity
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parsec
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subtends
Physics
Physics takes its place among the physical sciences with astronomy, chemistry, and geology, in dealing with natural phenomena concerning the behavior of inanimate objects, and some of its principles apply to living things as well. The fields of knowledge of these sciences overlap considerably and give rise to such branches as astrophysics, physical chemistry, geophysics, and biophysics. The laws and facts of Physics are concerned broadly with matter and energy, together with such related quantities as force and motion. These concepts and their inter-relations are fundamental to all parts of the subject, comprising mechanics of solids and fluids, heat, electricity and magnetism, sound, and light.
A definite knowledge of natural phenomena, and of the precise relations between them, is based upon experimental information concerning the quantities involved. If this information should be indefinite or ambiguous it would be subject to different interpretations, and naturally, the conclusions drawn therefrom would be open to much speculation. Clearly, the evidence obtained must be quantitative in order that it may have a definite meaning. Evidence of this type is obtained by measurement, one of the most important elements in all scientific work.
The usual way to measure a quantity is to compare it with some other quantity of the same kind which is used as a basis of comparison. Everyone is familiar with the process of measuring the length of an object by laying a foot-rule alongside it and expressing the result in feet and inches. A statement that a pole is 15 feet in length will give anyone having a foot-rule a correct picture of that length by laying off a distance equal to 15 one-foot distances. The length of the pole can also be expressed as 180 inches. This illustration shows that the measurement of a quantity involves two things; a number and a unit.To say that the pole measures 15 or 180 is an incomplete statement; it is necessary to say 15 feet or 180 inches. The unit shows how large a quantity is used as the basis of comparison, and the number shows how many of these units are contained in the quantity being measured.
Some statements based on physical measurements are given below to indicate the necessity for both number and unit: The rating of a certain automobile engine is 65 horsepower. The speed of a large steamship was found to be 25.3 knots. A Comfortable room temperature is 68 degrees Fahrenheit. Atmospheric pressure is about 14.7 pounds per square inch. The angular speed of a particular motor is 1800 revolutions per minute. The wavelength of yellow light is 0.0000589 centimeters. The charge of an electron is 1.60 X 10-19coulomb.
Physics is called an exact science because the quantities with which it is concerned are capable of accurate measurement. Accuracy in measurement requires knowledge of the correctness of the standard comparison, a measuring device of adequate sensitiveness, and care on the part of the operator in manipulation and computation.
Among the quantities which Physics deals, three are generally regarded as fundamental, namely, length, mass, and time.
Standards and Units of Length
The units of length commonly used belong to two groups, namely British Units and Metric Units, and these are based upon definite distances on bars that are preserved as standards. The yard is the standard length in the British group and is the distance at 62 degrees Fahrenheit (oF.) between two fine lines engraved on gold plugs in a bronze bar kept at the Standards Office in Westminster, London. The meter is the standard of length in the Metric Group and is the distance at degree centigrade (oC.) between the centers of two lines traced on a platinum-iridium bar kept in a subterranean vault of the International Bureau of Weights and Measures at Sevres, France. Several such standards are kept at the Bureau of Standards in Washington, D.C.
The multiples and sub-multiples of the yard and of the meter in common use are given below with their equivalents for reference purposes:
It is often necessary to convert expressions of length in one group to corresponding ones in the other group. The fundamental relationship between the yard and the meter, as fixed by the Act of 1866, is 1 yard = 3600/3937 meter. In consequence, the relations given above hold with sufficient exactness for most purposes.
At least the two relationships should be remembered.
In carrying out a computation involving lengths or other physical quantities, the units should be included throughout; they may be canceled, multiplied, or divided as though they were numbers. For example, find the number of kilometers in a mile by using the conversion factor 1 meter = 39.37 in. Since 5280 feet = 1 mile, the fraction 5280 feet/1 mile will have a value of unity, and the specified distance may be multiplied by this factor without altering its value. Three other fractions, each having a value of unity, are introduced in the same manner, and the entire solution is given by:
This procedure may seem laborious for such a simple computation, but in the more involved calculations, there is a distinct advantage in carrying all units through to avoid ambiguity and error.
Mass and its Measurement
It is assumed that all matter is composed of extremely small particles called molecules. All the molecules of a particular substance are, in general, alike and each consists of a definite structure of component parts; the structure of a molecule of one substance will, however, differ from that of another substance. Consequently, any particular object is composed of a definite quantity of matter determined by the number of molecules it contains and by the structure of the molecules themselves.
The term mass will be used for the present as a measure of the quantity of matter in a body. The British and Metric standards of mass are:
The kilogram of mass is defined as the mass of a certain block of platinum preserved at the International Bureau of Weights and Measures and known as the standard kilogram.
Other units of mass and the relations between them appear in the following table:
The measurement of mass is usually accomplished with an equal-arm balance, the mass to be measured is placed on one of its scale-pans, and known masses on the other, the latter being varied until a balance is obtained. The operating principle is in reality the balancing of two forces, the earth's attraction for the mass on one pan being just counteracted by the earth's attraction for the known masses on the other.
The mass of a substance per unit volume is known as its density, a dense substance being one in which a large quantity of matter occupies a small volume. A gallon of water is found to have a mass of 8.34 lb., and since its volume is 231 cu. in. = 0.1337 cu.ft., the density of water is 8.34 lb./0.1337 cu.ft. = 62.4 lb. per cu.ft. In metric units, it is 1 gm. per cu. cm.
Measurement of Time
The regularity of the earth's motion around the sun affords the basis for measurements of time. The earth revolves around the sun once a year (about 365 1/4 days). Its orbit or ecliptic is strictly an ellipse with the sun at one focus, but it may be considered approximately like a circle having a radius of 92,900,000 mi. The speed of the earth along this path varies slightly on account of the eccentricity of the orbit, the speed being greater where the earth is nearer the sun. The earth also rotates uniformly on its axis once a day. The axis passes through the north and south geographic poles, and is not perpendicular to the plane of the ecliptic but is inclined about 23.5o from a perpendicular position. The direction of the axis remains almost fixed in space as the earth rotates, and points almost directly toward the North Star, Polaris.
The stars are tremendously distant, the nearest star being many thousand times as far away as the sun. For this reason, the stars appear almost like fixed points in space, occupying virtually the same positions regardless of the position of the earth in its orbit. To us, it appears that the earth is stationary and that the sun and stars move. When one of the celestial bodies appears to pass through the plane of a given meridian it is said to cross the meridian.
If the instance that a given star crosses the meridian is recorded on two successive nights, the elapsed interval will be the time required for one complete rotation of the earth with reference to a star. This is called a sidereal day, and this constant interval is used in astronomical measurements. On the other hand, if the instance that the suncrosses the meridian are recorded on two successive days, the elapsed interval will be the time required for an apparent rotation of the earth with respect to the sun, and this is called a solar day. The solar days vary somewhat in length, the average throughout the year is known as the mean solar day. Through the course of a year, a given point on the earth is facing the sun 365 times must face a fixed point in space (i.e., a star) 366 times, and owing to this fact the mean solar day is about 366/365 of a sidereal day; that is, the mean solar day is about 4 min. longer than the sidereal day.
The mean solar day is subdivided into 24 hours, each hour being further divided into 60 minutes, and each minute into 60 seconds. Thus the mean solar day is composed of 86,400 mean solar seconds. This means solar second is the unit of time that is in general use for physical and engineering work, as well as for everyday purposes.
In spring-driven clocks or watches a gear train is allowed to run down at a slow and uniform rate under the action of an escapement, controlled either by a pendulum or a balance wheel, and the gear train turns the hands of the instrument in front of a dial or faceplate. In the synchronous electric clock, the hands are driven by a small motor that is connected to an alternating-current circuit and runs in synchronize with the generators at the power station, their speed is accurately controlled.
For the recording of official time, a precision clock is used, the accuracy of which is checked at regular intervals with a meridian telescope. Precision clocks are designed and constructed with the utmost care and are kept in constant-temperature rooms to insure uniform operation. The mechanism is enclosed in a glass case from which most of the air is removed. They are the most accurate timekeepers available.
In scientific and engineering work, it is usually desired to measure the duration of an interval of time rather than to determine the correct time at a certain instant. For this purpose, the familiar stopwatch is widely used. In laboratory work, clocks are used in which each sweep of the pendulum operates an electrical contact in a sounder circuit, the audible clicks of the sounder making the intervals easy to count. Short time intervals can be measured accurately by indirect methods that make use of tuning forks, chronographs, oscillographs, and crystals exhibiting the piezoelectric effect.
Using basic arithmetic and two simple equations anyone can become an astronomical genius.
Most people don’t realize how easy it is to calculate the paths of natural and man-made satellites. Rather than just Google these facts, it is far more satisfying to work them out for ourselves. Doing so will also help us to understand how gravity works, and how it keeps objects in orbit, as our planet around the Sun.
Two Equations and One Force
First, we need to understand the equation that determines the gravitational force between two objects. The larger object is usually called M because it has more mass, the smaller object is called m. The radius of the circle describing the orbit, which is also the distance between the centers of the two objects is called r. G is a constant or a number that is always of the same value when using metric unit measurements. Its purpose is to balance both sides of the equation.
This is the equation for the gravitational force or F:
F = GMm/r²
We only have to multiply G, M, and m together and then divide by r².
But there is another equation that describes the force acting towards the center of the circle that an object is circling. This is perfect for us because it describes well the gravitational force that pulls on an object in orbit.
Our second equation is F = mv²/r.
All the symbols are the same as in the first equation but now we also have the velocity of the orbiting object (v). We may intuitively understand this equation. If we have ever swung a ball on a rope around in a circle, we know that the faster it goes, the more force we have to exert on it to keep it from flying off. As the force in both equations is the same force, we can write:
mv²/r = GMm/r²
Simplifying Even Further Mbr>It’s getting even easier because after the cancellations (m/r is duplicated on both sides of the equation) we get:
v² = GM/r
Let’s use this simple equation to find Earth’s velocity or speed around the Sun.
v = vGM/r
Now, all we need to do is plug the numbers into this equation. The numbers are large, and some find them daunting. But even scientists and mathematicians are scared of big numbers, so they use a trick to cut them down to size. For example, instead of writing 1,000,000,000,000, they write 10¹², and this style of notation will make things a lot easier for us.
Crunching the Numbers
G = 6.672 x 10 ? ¹¹ (10 ? ¹¹ is the same as 1 divided by 10 ¹¹ )
The Sun’s mass, M = 1.989 x 10 ³º kilograms (now that is a big number)
Earth’s distance from the center of the Sun (average) = 1.496 x 10 ¹¹ meters.
V = v (6.672 x 10 ? ¹¹ x 1.989 x 10 ³º x (1/1.496) x 10 ? ¹¹)
V = 29,780 meters per second or 29.78 kilometers per second or 18.61 miles per second or 66,996 miles per hour.
A Greater Perspective
When we work out orbits for ourselves, it impresses upon us the orders of magnitude involved in our universe; imagine, the Earth is moving around the Sun at about 87 times the speed of sound! If we can become comfortable in our arithmetic using powers of ten, then the results can be truly astronomical.
Lesson Review
Directions: Follow the instructions in each Part below to complete the assignment. Remember to cite your resources. Citation examples are provided below the Review.
Part A
Directions: Answer each of the following questions.
1. The Mars Climate Orbiter crash was explained as being caused by a mix-up between metric and imperial units. The computer was programmed to work with pound weight (lbF) instead of newton. Given that the weight of 1 kg is equivalent to the weight of 2.2 pounds (lb), or 2.2 lbF, and that the weight of 1 kg (or 2.2 lbF) is 9.8 N:
a. Find the force in newtons of the weight of 1.0 lbF.
b. If the thrusters to put the craft into orbit were meant to use a value in N but used the same value in lb F, would they slow the craft more or less?
c. Analysis of the mission failure showed the thrusters force was 4.45 times too large, is the failure correctly explained by a unit mix-up?
2. Usain Bolt holds the world record for the 100 m sprint with a time of 9.58 s. His top speed is about 43.45 kmh-1.
a. What is Usain's average speed in...ms-1...kmh-1?
b. Why was his average speed less than his top speed?
c. How long would the race take if Usain had run at his top speed for the entire race?
3. It takes 40 N for Tamara to push a chair slowly and steadily across the carpet. She pushes the chair 4 m from one side of the room to the other.
a. How much work did Tamara do?
b. What happened to the work she did?
c. How could Tamar reduce the amount of work she is doing?
Part B
Directions: Answer each of the following questions.
1. Which of the following is true?
a. The earth revolves around the sun once a year.
b. The earth revolves around the sun for about 365 1/4 days.
c. Earth's orbit or ecliptic is strictly an ellipse with the sun at one focus.
d. The speed of the earth varies slightly on account of the eccentricity of the orbit.
e. All of these
2. The mean solar day is about __________ than the sidereal day.
3. Short time intervals can be measured accurately by indirect methods that make use of tuning __________.
4. The world land speed record is 763.0 mi/h, set on October 15, 1997, by Andy Green in the jet-engine car Thrust SS C. Express this speed in meters per second.
5. What is the quantity which Physics deals?
6. The accuracy of a precision clock is checked at regular intervals with _______________.
7. 1 meter = ________ in.
8. 1 yard = __________ meter.
9. What is used for the record of official time?
10. Any particular object is composed of a definite quantity of matter determined by _______________.
11. What is the basis for measurements of time-based on?
12. The tallest tree in the United States is Founder's Tree, a redwood in northern California. Its height is 364 ft. and its girth is 47.1 ft. Express these dimensions in meters.
13. 1 kilometer = _________ mile.
14. In scientific and engineering work, it is usually desired to measure the duration of an interval of time rather than to determine the correct time at a certain instant. What is it?
15. Which of the following is false about the precision clock?
a. Its accuracy is checked at regular intervals with a meridian telescope.
b. They are the least accurate timekeepers available.
c. Precision clocks are designed and constructed with the utmost care.
d. Precision clocks are kept in constant-temperature rooms to insure uniform operation.
e. It is used to record the official time.
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Let the rubric below guide your writing:
Rubric
- All responses must include complete sentences with supporting information from the lesson
- each response includes cited resources
- points are deducted if no resources are cited