Chapter 1 Introduction to Physics PDF

Chapter 1 Introduction to Physics PH 133 “Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.” Maire Curie (1867 - 1934)  Physics From the Greek wo...

Chapter 1 Introduction to Physics PH 133 “Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.” Maire Curie (1867 - 1934)  Physics From the Greek words physikos, "natural". The study of the behavior of the universe: – matter, energy, and time – fundamental laws of nature We will focus on the branch of physics called Mechanics: – the motion of objects and their response to forces.  Math and Physics In physics we attempt to describe the natural world through rules and mathematics. Math is the language of physics. We perform experiments to compare mathematical calculations to real life observations. We use mathematical equations to simulate and predict real life events. Units are very important in physics! We will primarily use the metric system. How many countries do not use the metric system? Three: United States Liberia Myanmar  Metric System Developed in France in 1790’s; used by most of the world. Based on set of common prefixes and powers of 10. Base Units: Length: meter (m); used like the foot. Mass: gram (g); used like the ounce. Time: second (s) Attach a prefix to a base unit to change the size of the unit. For example, if the base unit is a meter: 1 kilometer (km) = 1000 m 1 hectometer (hm) = 100 m 1 decameter (dam) = 10 m 1 meter = 10 decimeter (dm) 1 meter = 100 centimeter (cm) 1 meter = 1000 millimeter (mm) Notice the abbreviations.  Metric System Based on a set of common prefixes and powers of 10. Most common prefixes: kilo, hecto, deca, deci, centi, milli kilo (k) Down  Multiply by 10 for each step 1000 (of base unit) hecto (h) 100 deca (da) 10 base (meter, liter, or gram) 1 deci (d) 0.1 = 1/10 centi (c) 0.01 = 1/100 Divide by 10 for each step  Up milli (m) 0.001 = 1/1000  Metric Prefixes (full set) Prefix Symbol Equivalent (compared to base unit) yotta Y 1 Y = 1 000 000 000 000 000 000 000 000 (1024) base units zetta Z 1 Z = 1 000 000 000 000 000 000 000 (1021) base units exa E 1 E = 1 000 000 000 000 000 000 (1018) base units Larger than base unit peta P 1 P = 1 000 000 000 000 000 (1015) base units tera T 1 T = 1 000 000 000 000 (1012) base units giga G 1 G = 1 000 000 000 (109) base units mega M 1 M = 1 000 000 (106) base units kilo k 1 k = 1 000 (103) base units hecto h 1 h = 100 (102) base units deca da 1 da= 10 (101) base units For smaller units, base 1 base = 1 (100) base units use these equivalents: deci d 1 d = 0.1 (10-1) base units 1 base = 10 d centi c 1 c = 0.01 (10-2) base units 1 base = 100 c Smaller than base unit milli m 1 m = 0.001 (10-3) base units 1 base = 1000 m micro µ 1 µ = 0.000 001 (10-6) base units 1 base = 10-6 µ nano n 1 n = 0.000 000 001 (10-9) base units 1 base = 10-9 n pico p 1 p = 0.000 000 000 001 (10-12) base units 1 base = 10-12 p femto f 1 f = 0.000 000 000 000 001 (10-15) base units 1 base = 10-15 f atto a 1 a = 0.000 000 000 000 000 001 (10-18) base units 1 base = 10-18 a zepto z 1 z = 0.000 000 000 000 000 000 001 (10-21) base units 1 base = 10-21 z * yocto y 1 y = 0.000 000 000 000 000 000 000 001 (10-24) base units 1 base = 10-24 y Once out the of most common prefix range, jump by 103. Some common metric prefixes: Name Abbreviation Amount of base units Tera T 1012 Giga G 109 Mega M 106 Kilo k 103 Hecto h 102 Deca da 101 Deci d 10−1 Centi c 10−2 Milli m 10−3 Micro 𝜇𝜇 10−6 Nano n 10−9 Pico p 10−12  Measurements and Unit Conversion Every measurement consists of 2 parts: a number and a unit. For example, 25 ft. To convert units, use ‘unit fractions’. A unit fraction has a value of 1. Numerator and denominator contain different units, but are equal. Unit Conversion: 1. Write original quantity as a fraction. 2. Create a unit fraction using equivalent units. 12 in 1 ft For example,12 in = 1 ft; unit fraction is or. 1 ft 12 in Set up so that the unit not wanted cancels out. 3. Multiply the fractions: numerators across and denominators across. Reduce numbers.  Example Convert 36 m to cm 36 m 100 cm ∗ = 3,600 cm 1 1m Convert 1 yd2 to ft2 1 yd2 3 ft 3 ft ∗ ∗ = 9 ft 2 1 1 yd 1 yd Convert 10.0 mph to m/s 10.0 mi 1 hr 1 min 1609 m ∗ ∗ ∗ = 4.47 m/s hr 60 min 60 sec 1 mi  Dimensional Analysis The dimension is a type of quantity. It is not tied to a specific unit. Basic dimensions for our course: Length [ L ] Mass [ M ] Time [ T ] Any valid formula must be dimensionally consistent. All terms in an equation must have the same dimension. Remember can only add like terms. The numbers in an equation do not affect the dimension and can be ignored. 1 𝐴𝐴 = 𝑏𝑏𝑏 Area units [L2]. Both left and right sides are [L2] 2 Can also use units when checking dimensions. For example, instead of [L] use m. Example Is this equation dimensionally correct? V = lwh Solution: [L]3 = [L][L][L] [L]3 =[L]3 OK! What dimension must “t” be if x has the dimension of length and v has the dimension of length/time? x = xo + vavgt Solution: 𝐿𝐿 𝐿𝐿 = 𝐿𝐿 + ⋅? [𝑇𝑇] t must have a dimension of time to cancel the [T] and have all the terms as [L].  Standard SI Units SI: System International Although there are many types of units for a given “dimension”, there is a set of standard units used in this class. We will use the SI system of the metric system, established by an international committee in 1960. Dimension SI Standard Unit Abbreviation Length [L] meter m Mass [M] kilogram kg Time [T] second s Note: If a measurement is not in these units, may need to convert before doing calculations. SI standard units are not always the base units of the metric system.  quantity dimension SI units area [ L ]2 m2 volume [ L ]3 m3 velocity [ L ] / [T] m/s acceleration [ L ] / [ T ]2 m/s2 mass [M] kg  Example The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: speed of light c = 3.00 × 108 m/s, gravitational constant G = 6.67 × 10−11 m3/(kg ⋅ s2), Planck's constant h = 6.63 × 10−34 kg ⋅ m2/s. The Planck length ℓP is given by the following equation: 𝐺𝐺𝐺 ℓ𝑃𝑃 = 𝑐𝑐 3 Show that the dimensions of ℓP are length [L]. (The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate.)  Example Solution Although the dimension is not tied to a specific unit, if the units for each dimension match, you may use units to perform the dimension check. (Often easier to write units.) 𝐺𝐺𝐺 ℓ𝑝𝑝 = 𝑐𝑐 3 1 2 1 2 𝑚𝑚3 𝑘𝑘𝑘𝑘𝑚𝑚 𝑚𝑚5 2 1 2 𝑠𝑠 𝑚𝑚5 𝑠𝑠 3 2 𝑘𝑘𝑘𝑘𝑠𝑠 𝑠𝑠 3 𝑚𝑚 =? =? =? 3 𝑚𝑚 3 𝑚𝑚 3 3 𝑠𝑠 𝑚𝑚 𝑠𝑠 𝑠𝑠 1 =? 𝑚𝑚2 2 = 𝑚𝑚 Okay!  Order-of-Magnitude An order-of-magnitude calculation is a estimate designed to be accurate within a factor of about 10. One purpose is to provide a quick idea of what should be expected from a calculation. The answer is reported as 10𝑥𝑥 , where 𝑥𝑥 is an integer. (10 to a power) Example Estimate how much water there is in a particular lake (in m3), which is roughly circular, about 1 km across, and has an average depth of about 10 m. (For HW, may need to look up values for order-of-magnitude problems. This is an estimate so do not need exact values.)  Example solution Solution:  Accuracy and Precision Careful measurements are very important in experiments so that the error is minimized and results are reproducible. Accuracy: How close a measured value is to the true value. Poor accuracy involves errors that can often be corrected, such as reading the instrument incorrectly. Precision: How exact a measured value is based on the measuring device. Limited by smallest division of the measuring device. To measure precision read to smallest division, and estimate one additional decimal place. For lab, all measurements must have the correct precision.  Precision To measure precision, read to smallest division and estimate one additional decimal place. Smallest measure = 1 mm. One additional decimal place = 0.1 mm Ruler: Precision is 0.1 mm = 0.01 cm = 0.0001 m Smallest measure = 0.1 g. One additional decimal place = 0.01 g Triple beam balance: Precision is 0.01 g = 1 cg = 0.00001 kg  Significant Digits Precision indicates the number of significant digits. These are the number of reliably known digits. Significant Digits are: Non-zero digits 12.5 Trailing zeros in the decimal portion 12.50 Zeros between non-zero digits 120.5 Non-significant Digits: Zeros in front of non-zero digits 0.00125 Zeros behind non-zero digits to the left of the decimal point 12500 If want to show all digits of 12,500 are significant, use scientific notation: 1.2500 x 104. Operations with Significant Digits Addition/subtraction: Round answer to the least number of decimal places found in the original numbers. Multiplication/division: Round answer to the least number of significant figures found in the original numbers. When have multiple types of operations, keep all digits and round to the least number of significant digits in the original numbers at the end.  Examples: (Follow standard rules for rounding, as needed.) 1. How many significant figures are in the number 10001? 2. How many significant figures are in the number 0.01500? 3. How many significant figures are in the number 100? 4. How many significant figures are in the number 1.00 x 102? 5. What is the difference between 103.5 and 102.24? 6. What is the product of 12.56 and 2.12? Answers 5 4 1 3 103.5-102.24=1.26. Round to 1.3 12.56x2.12=26.6272. Round to 26.6