## P-1 CALCULATION EXERCISES1. BACKGROUND
Your textbook probably contains a discussion of the metric System, unit conversions, and exponential notation. Further discussion of these topics will be found in the appendices of this lab manual. The student should become familiar with this material before coming to lab. A more detailed reference which some students may find helpful throughout the course
is:
Kruglak and Moore,
This exercise is a problem session rather than a laboratory investigation. Its purpose is to make sure that all students can to do the fundamental mathematical manipulations required in this course. The problems are graded in difficulty, and should therefore be done in order. There are enough problems so that even the fastest student will be occupied most of the period. Do not rush to finish--be sure you understand each problem before proceeding to the next. If you are stumped on a problem, ask the instructor to discuses it with you, for he may give you some hints. Feel free to discuss the problems with your lab partner, but share the work. To prevent confusion in the lab room, do not extend the discussions to other groups. We will follow this rule throughout the course.
(1) If you are unfamiliar with metric length measurements, first examine a meter stick to learn the meaning of its markings. The meter stick is subdivided into 100 marked divisions called centimeters. Each centimeter is subdivided into 10 very small divisions called millimeters. What are the smallest divisions marked on the meter stick? How are the decimeters marked? (2) Use a meter stick to measure the length and width of a lab table top. Devise some way to minimize the uncertainty due to the rounded edges of the table. Calculate the surface area of the table, and express this answer in three ways: square centimeters, square meters, and square millimeters. (3) Devise a way to determine the thickness of the paper of a page of your textbook. How much uncertainty does this measurement have?
* Adapted in part from Pauling, 4. PROBLEMS
Express all answers in exponential notation in standard form, rounded to the appropriate number of significant figures. (1) Calculate the number of cubic centimeters in a cubic meter. (The answer is
(2) A classroom has dimensions of 5.8 meters, 10.2 meters, and 3.5 meters. Calculate the volume of the room in cubic meters. (3) Use the result of problem 2 to calculate the number of cubic centimeters in the room
described in problem 1. Then check this answer by first converting the room dimensions to
centimeters, (4) How many cubic centimeters are in a cubic kilometer? Since this is a large number, express it in exponential notation. (5) One light year is the
(A1) For expressing very large numbers, the unit (A2) The (A3) Find the sine of 0.0001 degree to three significant figures. How much more precisely could you determine this?
(A4) An article about prime numbers in the Scientific American magazine of March, 1964 mentions that "The Computer Division of Los Alamos has a magnetic tape on which 20 million prime numbers are recorded." Suppose we wanted to print all of these numbers in a book. A moderate speed computer printer can print about 200 lines per minute. If one prime number were printed per line, how long would it take to print all those prime numbers? Express the answer in days, or years, whichever is more appropriate. If the printout has 60 numbers per sheet of paper, how thick would be the stack of sheets? If reproductions were made and sold at typical "textbook" prices, how much would a copy cost? (A5) If we made a scale model of the earth the size of a bowling ball, how high would
Mount Everest be on the model, in inches? In cm? The earth's radius is 6.4 x
10
(Bl) The estimated amount of hydrogen in interstellar space is one atom per cubic centimeter. Our galaxy is shaped somewhat like a round disk, with a diameter of 300,000 light years and a thickness of 35,000 light years. Approximately how many atoms of interstellar hydrogen are there in our galaxy? (The data is only accurate to one significant figure, so express the answer accordingly.) (B2) What is the mass of one cubic centimeter of water at a temperature of 20°C? [Look this up in a reference book.] In elementary chemistry
and physics lab work this is often taken to be approximately 1 gm/cm (B3) Masses of atoms are measured using a unit called the unified atomic mass (u)
defined so that the mass of the isotope Carbon-12 (
(B4) A flea can jump over a foot upward. If you could jump that well, relative to your size, how high could you jump? (B5)
(C1) In the chart on page 3 of this experiment, the distance to the farthest known galaxy is shown. Check the consistency of this value with the value given in the footnote on page 2. (C2) The unit of mass in the metric system was chosen so that the density of water would
be 1 gm/cm
(C3) If you drew a "picture" of an atom one inch in diameter, how large would you have to draw the nucleus? Compare your conclusion with pictures of atoms you have seen in textbooks. Consider drawing a scale model of the solar system with the orbit of Pluto five inches in diameter. How large would the sun be on this picture? Compare with the pictures you have seen. (C4) In elementary science books, the atom is often described as a "miniature solar system." Consult the chart of page 3 of this experiment along with the results of problem C3 to determine whether this statement is an accurate analogy, at least with respect to the sizes of the component parts of the system. (C5) The German philosopher Friedrich Wilhelm Nietzsche (1844-1900) said "The earth has a skin and that skin has diseases; one of its diseases is called man." Physicist Albert Abraham Michelson (1852-1931) told his students (at the University of Chicago) that mankind as a whole was rather insignificant on a universal view, merely "a skin disease upon the face of the earth." Consult the chart of sizes to determine whether this statement is an accurate comparison of relative sizes.
(D1) Gerald Holton, Derek J. de Solla Price end others have estimated that "80 to 90 per cent of all scientists that have ever been, are alive now." Should this surprise anyone? How would this ratio compare with other professions? With the general population? Discuss, citing appropriate data from library research. (D2) Theodor Rosebury, in his fascinating book (D3) (a) Find out the top speed of a garden snail moving across the ground in search of juicy leaves to munch on (a snail's-pace). (b) Express this snail's pace in centimeters per second. (c) Express this also in the units furlongs/fortnight. Text © 1997, 2004 by Donald E. Simanek. |