Chapter 1 | Physical and Measurements |

| SUMMARY | | * Physical quantity is a quantity that can be measured. * Table 1.1 shows two types of physical quantities:Table 1.1 : Two types of physical quantities Basic quantities | Derived quantities | - fundamental physical quantities- examples: length, mass, temperature and etc. | - combination of several basic quantities- examples: acceleration, force, volume and etc. | * Units are standardized quantities we use to compare our measurements against. * In physics, a standard system of units based on metric system is known as the Systẻme International d’Unitẻs or SI. * SI uses seven base units including meter (m), kilogram (kg), and second (s) for physical quantities length, mass and time, respectively. * Large values in SI unit are normally written in powers of ten. * Another way in writing units in powers of ten is by using prefixes. * Table 1.2 shows some of the powers of ten and the SI unit prefixes used for them.Table 1.2 : SI Prefixes Power of ten | Prefix | Symbols | 10-18 | Atto | a | 10-15 | Femto | f | 10-12 | Pico | p | 10-9 | Nano | n | 10-6 | Micro | µ | 10-3 | Mili | m | 10-2 | Centi | c | 103 | Kilo | k | 106 | Mega | M | 109 | Giga | G | 1012 | Tera | T | 1015 | Peta | P | 1018 | Exa | E | * Significant figures are number of meaningful digits in a numerical quantity. * A significant figure is one that is reliably known * Nonzero digits are always significant. * Zeros are significant when: * when they are placed between other non-zero digits * If placed after the decimal point and another significant figure * if clarified by using scientific notation. | | Example 1.1 | For each of these values, identify the number of significant figures and rewrite it in standard scientific notation.a) 875.0 x 101 mL b) 9280 g c) 0.012300 cm d) 510.2 s Solution: a) Four significant figures. Scientific notation: 8.75 x 103 mL b) Four significant figures. Scientific notation: 9.28 x 103 g c) Five significant figures. Scientific notation: 1.23 x 10-2 cm d) Four significant figures. Scientific notation: 5.102 x 102 s | Example 1.2 | | The radius of our earth is approximately 6.37 x 106 m. a) What is its circumference in kilometers? b) What is its surface area in square kilometers? c) What is its volume in cubic kilometers?Solution: a) Circumference = 2πr = 2π (6.37 x 106) = 4.00 x 107 m = 4.00 x (107 m) x ( 1 km ) (1000 m) = 4.00 x 104 km b) Surface area= 4πr2 = 4π(6.37 x 106)2 = 5.0997 x 1014 m2 = 5.0997 x 1014 m2 x ( 1 km )2 (1000 m)2 = 5.0997 x 1014 x 10-6 km2 = 5.0997 x 108 km2 c) Volume = 4 πr3 = 4 π(6.37 x 106)3 = 1.0828 x 1021 m3 3 3 = 1.0828 x 1021 m3 x ( 1 km )3 (1000 m)3 = 1.0828 x 1021 x 10-9 km3 = 1.0828 x 1012 km3 | | Exercise 1.1 | How much does a 2 liter bottle of soda pop weigh in pounds? (Assume that the pop has the density of water, namely 1 kg.liter-1, and that the weight of the bottle itself is negligible.)
(1 kg = 2.2 lb mass) a) 4.4 pounds. b) 4.5 pounds. c) 4.3 pounds. d) 4.6 pounds. | Exercise 1.2 | Which is faster, 60 miles per hour or 60 feet per second?
(1 mi = 5280 ft; 1 hr = 3600 sec.) a) 60 mi.hr-1 b) 60 ft.sec-1 | Exercise 1.3 | | A 5 gallon bucket of tar weighs 30-lb. What is the mass of the bucket in SI units (kg)? Given 1 kg equivalent to 2.2046 lb mass. a) 13.61 kg b) 11.61 kg c) 13.16 kg d) 16.21 kg | | Exercise 1.4 | For the same bucket as above, what is the volume in SI units (m3)?. Given 1 m3 is equal to 264.172 gallons. a) 0.091 m3 b) 0.019 m3 c) 0.109 m3 d) 0.190 m3 | Exercise 1.5 | Convert 10 km.(hr.s)-1 to m.s-2 a) 2.89 m.s-2 b) 3.78 m.s-2 c) 2.78 m.s-2 d) 3.89 m.s-2 | Exercise 1.6 | A basketball hoop is 10 ft above the playing floor. What is the height of the hoop from the floor in m? Given 1 ft = 0.3048 m.Solution: | Exercise 1.7 | | Nonzero digits are always significant figures? True/FalseThe leading zeros are significant figures? True/FalseZeros between two other significant digits are always significant? True/FalseZeros used solely for spacing the decimal point are significant? True/False | Exercise 1.8 | The following equation describes the motion of an object. What must the units be for the variables A, B, and C? (Assuming x is displacement and t is time) Solution: | Exercise 1.9 | | A baseball is thrown at 95 mi.hr-1. Convert this value to m.s-1 using 1 mi = 1609 m.Solution: | | Exercise 1.10 | How many cubic meters are there in a cubic mile? (1 mi = 1609.344 m)Solution: | Model Examination Question 1.1 | PART AExpress the following quantities in terms of S.I. units: a) 256.7 mg.cm-3 [2 marks] b) 78.1 nm.s-1 [2 marks]Solution: | | Model Examination Question 1.2 | PART A a) What are the four basic physical quantities? [2 marks]b) A cylindrical water tank holds 636 L of water. The volume of a cylinder is given by V = πr2h. How much water (in L) could the tank hold if the radius was doubled? [2 marks]Solution: | Model Examination Question 1.3 | PART AThe density of aluminum is 900 Ib.ft-3 (in U.S Units). Given 1 Ib mass = 0.454 kg, 1 ft =12 in and 1 in = 2.54 cm. Express this density value in: a) g.cm-3 [2 marks]b) kg.m3 [2 marks]Solution: | Model Examination Question 1.4 | PART AChange the followings to the SI unit and in standard form: a) 2.31 MJ [2 marks]b) 1.5 g.cm-3 [2 marks]Solution: | Model Examination Question 1.5 | PART Aa) What are basic and derived quantities? [2 marks]b) Given Z = kQ.r-2, if Z was 29.3 when r was 13.5, what would Z be if r was doubled? [2 marks]Solution: |