PROBLEMS IN ELEMENTARY PHYSICS. CHAPTER I. METRIC SYSTEM. 1. The Metric System is a system of weights and measures based upon a decimal system of notation. Its use in physical science has now become almost universal. Its use in commerce is increasing slowly. The two following pages contain all that a beginner in Physics need know of the metric system. A few equivalents for changing quantities from one system to the other are also given. Units most important in the laboratory are given in small capitals. Measures of Length. 10 MILLIMETERS (mm.) = 1 CENTIMETER (cm.) 10 centimeters 10 decimeters 10 meters 10 decameters = 1 decimeter (dm.) 1 decameter (Dm.) Measures of Surface. (The square surfaces from the mm., cm., and m. only are 10 milligrams (mg.) = 1 centigram (cg.) 10 centigrams 10 decigrams = 1 decigram (dg.) = 1 GRAM (gm.) 1000 gm. = 1 KILOGRAM (kgm.) or KILO. NOTE.--The equivalents for square and cubic measures are seldom needed. They may be obtained from those for linear Area of circle R'; surface of sphere 47 R2 or π D2. C. 1 gm. Weight of 1 cu. cm. pure water at 4° Weight of 1 cu. ft. pure water at 4° (nearly). C. = 62.5 lbs. Weight of 1 liter (1000 cu. cm.) air at 0° C. and 76 cm. mercury pressure = 1.293 gm. Length of seconds pendulum at New York = 99.317 cm. or 39.1 inches. Value of "g" at New York = 980 cm. or 32.16 ft. STANDARD CONDITIONS for a gas are that the pressure equal that of a column of mercury 76 cm. in height and the temperature be 0° C. 4. The Meter is one ten-millionth of the distance from the equator to either pole of the earth. The measurements to determine this were made in 1799, and subsequent calculations have shown the standard meter to be a very small fraction smaller than this one ten-millionth. The FRACTIONAL parts of a meter, gram, etc., are expressed by the use of Latin prefixes. The MULTIPLES are expressed by the use of Greek prefixes. The Gram is the weight of 1 cu. cm. of pure water at the temperature at which it is densest, namely, 4° C. (39.2 Fahrenheit). 1. METRIC SYSTEM. 1. What is the unit of length in this system? 2. What is the meter with reference to the earth's circumference? 3. What is the unit of square measure ? 4. What is the unit of cubic measure? 5. When you reduce square meters to square centimeters, by what number do you multiply? 6. When you reduce cubic decimeters to cubic meters, by what number do you divide? 7. What is the unit of weight? 8. How was this unit chosen ? 9. What name is given to 1000 m.? to 1000 gm.? 10. Change 180 sq. m. to sq. mm. 11. Change 6721 m. to km. 12. In 9.1 cu. m. how many cu. cm.? 13. Change 7.15 sq. cm. to sq. m. 14. Change 21.5 kgm. to gm. 15. If mercury weighs 13.6 times as much as water, what is the weight of 15 cu. cm. of mercury? 16. A tank is 7.6 m. by 3.8 m. by 4.3 m. kgm. of water will it hold? 17. What is a liter? 18. How many liters in 105 cu. m.? 19. Express the ratio of the cm. to the inch. How many (In this and other questions involving both English and metric units see Table of Equivalents on pages 2 and 3.) 20. 76 cm. equals how many inches? 21. How many times heavier is the ounce (avoirdupois) than the gram? 22. If 1 kgm. = 2 lbs., how many kgm. are there in a ton? 23. How many kgm. in 62.5 lbs.? 24. How many ounces in 1 kgm.? 25. How many meters in 34 ft.? NOTE. When the metric units are used, always use decimal fractions. When English units are employed, common fractions are usually the more convenient. |