Physics and Measurement
1
Physics and Measurement
CHAPTER OUTLINE
1.1 1.2 1.3 1.4 1.5 1.6 1.7 Standards of Length, Mass, and Time Matter and Model-Building Density and Atomic Mass Dimensional Analysis Conversion of Units Estimates and Order-ofMagnitude Calculations Significant Figures
ANSWERS TO QUESTIONS
Q1.1 Q1.2 Atomic clocks are based on electromagnetic waves which atoms emit. Also, pulsars are highly regular astronomical clocks. Density varies with temperature and pressure. It would be necessary to measure both mass and volume very accurately in order to use the density of water as a standard. People have different size hands. Defining the unit precisely would be cumbersome. (a) 0.3 millimeters (b) 50 microseconds (c) 7.2 kilograms (b) and (d). You cannot add or subtract quantities of different dimension. A dimensionally correct equation need not be true. Example: 1 chimpanzee = 2 chimpanzee is dimensionally correct. If an equation is not dimensionally correct, it cannot be correct.
Q1.3 Q1.4 Q1.5 Q1.6
Q1.7
If I were a runner, I might walk or run 10 1 miles per day. Since I am a college professor, I walk about 10 0 miles per day. I drive about 40 miles per day on workdays and up to 200 miles per day on vacation. On February 7, 2001, I am 55 years and 39 days old. 55 yr
Q1.8
F 365.25 d I + 39 d = 20 128 dFG 86 400 s IJ = 1.74 × 10 GH 1 yr JK H 1d K
9
s ~ 10 9 s .
Many college students are just approaching 1 Gs. Q1.9 Q1.10 Q1.11 Zero digits. An order-of-magnitude calculation is accurate only within a factor of 10. The mass of the forty-six chapter textbook is on the order of 10 0 kg . With one datum known to one significant digit, we have 80 million yr + 24 yr = 80 million yr.
1
2
Physics and Measurement
SOLUTIONS TO PROBLEMS
Section 1.1 Standards of Length, Mass, and Time
No problems in this section
Section 1.2 P1.1
Matter and Model-Building
From the figure, we may see that the spacing between diagonal planes is half the
Physics and Measurement
CHAPTER OUTLINE
1.1 1.2 1.3 1.4 1.5 1.6 1.7 Standards of Length, Mass, and Time Matter and Model-Building Density and Atomic Mass Dimensional Analysis Conversion of Units Estimates and Order-ofMagnitude Calculations Significant Figures
ANSWERS TO QUESTIONS
Q1.1 Q1.2 Atomic clocks are based on electromagnetic waves which atoms emit. Also, pulsars are highly regular astronomical clocks. Density varies with temperature and pressure. It would be necessary to measure both mass and volume very accurately in order to use the density of water as a standard. People have different size hands. Defining the unit precisely would be cumbersome. (a) 0.3 millimeters (b) 50 microseconds (c) 7.2 kilograms (b) and (d). You cannot add or subtract quantities of different dimension. A dimensionally correct equation need not be true. Example: 1 chimpanzee = 2 chimpanzee is dimensionally correct. If an equation is not dimensionally correct, it cannot be correct.
Q1.3 Q1.4 Q1.5 Q1.6
Q1.7
If I were a runner, I might walk or run 10 1 miles per day. Since I am a college professor, I walk about 10 0 miles per day. I drive about 40 miles per day on workdays and up to 200 miles per day on vacation. On February 7, 2001, I am 55 years and 39 days old. 55 yr
Q1.8
F 365.25 d I + 39 d = 20 128 dFG 86 400 s IJ = 1.74 × 10 GH 1 yr JK H 1d K
9
s ~ 10 9 s .
Many college students are just approaching 1 Gs. Q1.9 Q1.10 Q1.11 Zero digits. An order-of-magnitude calculation is accurate only within a factor of 10. The mass of the forty-six chapter textbook is on the order of 10 0 kg . With one datum known to one significant digit, we have 80 million yr + 24 yr = 80 million yr.
1
2
Physics and Measurement
SOLUTIONS TO PROBLEMS
Section 1.1 Standards of Length, Mass, and Time
No problems in this section
Section 1.2 P1.1
Matter and Model-Building
From the figure, we may see that the spacing between diagonal planes is half the