Lecture Outline. I. Fundamental Measurements II. Unit Conversion Level I: Motion (Treat the levels as practice exams)
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1 Planning Ahead Be able to distinguish between velocity and acceleration. Learn the format of the Physics solution. Learn how to overcome the difficulties in graphs.
2 Lecture Outline I. Fundamental Measurements II. Unit Conversion Level I: Motion (Treat the levels as practice exams)
3 Study Guide The best way to learn Physics is to become a Physics tutor. Get into a study group. The act of explaining physics to someone is the best study and learning method. Develop good habits. What you are use to doing is what you will resort to when stressed or panicking.
4 Lecture Goals By the time you leave today, you should understand how to covert units. Be able to identify mistakes in equations and how to fix them.
5 Improving Your Grade 1. Exercise 2. Eat a healthy diet 3. Sleep more hours 4. Avoid the comfort zone 5. Be Happy
6 Extra Credit Student who submits the most amount of extra Homework solutions. Student who gets the most amount of participation points. Student who invents the most promising Physics 125 invention. Win the Project competition.
7 I. Fundamental Measurements Dimensions Length SI units (m) meter Time (s) second Mass (kg) kilogram
8 Unit Algebra Drill/Due Today mm ss mm ss mm ss 2 ss = 1 ss = kkkk ss =
9 Dimensions Drill/Due Today Length also can have units of: A. Pounds B. Feet C. Celsius D. None of the above
10 Dimensions Drill/Due Today Mass also can have units of: A. Pounds B. Feet C. Celsius D. None of the above
11 Reading Between the Lines I cdnuolt blveiee that I cluod aulacity uesdnatnrd what I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtsity... xx ff = 1 2 aa xxtt + vv iiii + xx ii
12 Dimensions Drill/Due Today Velocity mm SI units A. B. C. m D. None ss Dimensions lllllllllll tttttttt mm ss 2
13 Dimensions Drill/Due Today Acceleration mm A. B. C. m D. None ss Dimensions SI units lllllllllll tttttttt 2 mm ss 2
14 Classical Mechanics Dimensions xx = yy If x has dimensions of length, then y must also have dimensions of length. vv = aaaa If v has dimensions of length/time, then at must have dimensions of.
15 Dimensions Drill/Due Today xx = ββtt If x has dimensions of length and t has dimensions of time, then what must be the dimensions of β? A. length B. length/time C. length/time 2 D. None
16 Dimensions Drill/Due Today vv = aaaa If v has dimensions of length/time and t has dimensions of time, then what must be the dimensions of a? A. length B. length/time C. length/time 2 D. None
17 Dimensions Drill/Due Today vv = aaaa + KK + HH If v has dimensions of distance/time, then what are the dimensions of K and H? A. length B. length/time C. length/time 2 D. None
18 Dimensions Drill/Due Today mm = mm ss 2 + mm ss 4 + mm ss mm = mm ss 2 ss2 + mm ss 4 ss4 + mm ss ss xx = αα tt 2 + ββ tt 4 + γγ tt xx = 4 mm ss 2 tt2 + 3 mm ss 4 tt4 + 6 mm ss tt
19 Dimensions Drill/Due Today xx = ααtt 3 + ββtt + γγ If x has dimensions of distance and t has units of seconds, then what is/are the dimensions γ? A. length B. length/time C. length/time 2 D. None
20 Dimensions Drill/Due Today xx = ααtt 3 + ββtt + γγ If x has dimensions of distance and t has units of seconds, then what is/are the dimensions of β? A. length B. length/time C. length/time 2 D. None
21 Dimensions Drill/Due Today xx = ααtt 3 + ββtt + γγ If x has dimensions of distance and t has units of seconds, then what is/are the dimensions of α? A. length B. length/time C. length/time 2 D. None
22 Dimensions Drill/Due Today vv = ααtt 5 + ββ tt + sin γγ If v has dimensions of distance/time and t has units of seconds, then what are the dimensions of α, β, and γ?
23 Dimensions Drill/Due Today xx = ααtt 3 + ββtt + γγ If x has dimensions of distance and t has units of seconds, then what is/are the dimensions of β? A. length B. length/time C. length/time 2 D. None
24 Critical Thinking Drill/Due Today xx = vv x has units of m and v has units of m/s, If the units are correct, then there is a mistake in the equation. Find the mistake and make the correction.
25 Recall: Reading Between the Lines I cdnuolt blveiee that I cluod aulacity uesdnatnrd what I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtsity... xx ff = 1 2 aa xxtt + vv iiii + xx ii
26 Critical Thinking Drill/Due Today xx ff = 1 2 aa xxtt + vv iiii + xx ii x has units of m and a x has units of m/s 2, v ix has units of m/s, and x i has units of m. If the units are correct, then there are mistakes in the equation. Find the mistakes and make the correction.
27 Critical Thinking Drill/Due Today xx = ααtt 3 + ββtt + γγ x has dimensions of distance and α has units of m/s 2, β has units of m/s, and γ has units of m. If the units are correct, then there are mistakes in the equation. Find the mistakes and make the correction.
28 Critical Thinking Drill/Due Today xx = ααtt 3 + ββtt + γγ x has dimensions of distance and α has units of ms 2, β has units of m/s 3, and γ has units of m/kg. If the units are correct, then there are mistakes in the equation. Find the mistakes and make the corrections.
29 Critical Thinking Drill/Due Today vv = ααtt 5 + ββ tt + sin γγ If v has dimensions of distance/time and t has units of seconds, α = 5 m/s 2, β = 4 kg, and γ = 3 m/s. If the units are correct, then there are mistakes in the equation. Find the mistakes and make the corrections.
30 Critical Thinking Drill/Due Today xx = ααtt 7/2 + ββ tt + sin γγ + ee iiωωtt If x has dimensions of distance and t has units of seconds, then what are the units of α and ω? If β = 5 kg/s, and γ = 3 then find the mistakes in the equation and make the corrections.
31 Critical Thinking Drill/Due Today The units are correct FF = kk QQ rr FF haaaa uuuuuuuuuu oooo kkkk mm ss 2 kk haaaa uuuuuuuuuu oooo kkkk QQ haaaa uuuuuuuuuu oooo CC rr haaaa uuuuuuuuuu oooo mm mm 3 ss 2 CC 2
32 II. Unit Conversion Examples of units: 7 feet, 2 meters, 4 seconds, 5 grams, 9 pounds, 65 mph etc. Reasons for studying Unit Conversion: 1. Textbook problems often require unit conversions. 2. Convert units in workplace.
33 Importance of Correct Unit Conversion NASA's metric confusion caused Mars orbiter loss NASA's Climate Orbiter was lost September 23, 1999 September 30, 1999 Web posted at: 1:46 p.m. EDT (1746 GMT) (CNN) -- NASA lost a $125 million Mars orbiter because one engineering team used metric units while another used English units for a key spacecraft operation, according to a review finding released Thursday. Did you do the Assessment?
34 Unit Conversion Conversion Factor Found in textbook cover or appendix Equation for unit conversion: Starting Unit [Conversion Factor] = Desired Unit
35 Money Conversion EEEEEE UUUUUU =1.1531
36 Cutnell s Cover page
37 Visualization Solution km miles 1 mile is approximately 1.6 km.
38 Visualization Drill/Due Today km miles Based on the graph, 5 miles is approximately how many kilometers?
39 Visualization Drill/Due Today km miles Based on the graph, 3.5 miles is approximately how many kilometers?
40 Reasoning Solution A. [ 1 in = 2.54 cm] B. [1 hour = 3600 s] C. [1 mph = m/s] D. [1 lb = 4.45 N] Which conversion will you pick to convert time?
41 Reasoning Drill/Due Today A. [ 1 in = 2.54 cm] B. [1 hour = 3600 s] C. [1 mph = m/s] D. [1 lb = 4.45 N] Which conversion will you pick to convert speed?
42 Critical Thinking Drill/Due Today [ 1 in = 2.54 cm] [1 hour = 3600 s] [1 mph = m/s] [1 lb = 4.45 N] Is there enough information to determine the number of meters in a mile? If yes, what is that conversion factor?
43 A brief history of the meter. 1. Length
44 Length Conversion Math Solution We want to convert 12 in. into cm 1.) Write down 12 in. 2.) Look for the conversion factor in the book.
45 Cutnell s Cover page
46 Length Conversion 1 in = 2.54 cm From appendix Treat the units like an algebraic variable 1in 12in 2.54cm = 4.7 in 2 cm 12in 2.54cm 1in Assess the numbers. = 30.4cm
47 Math Drill/Due Today We want to convert 17 in. into cm 1 in = 2.54 cm
48 Math Drill/Due Today We want to convert 10 cm. into in 1 in = 2.54 cm
49 Assessment Solution cm number is larger than the inch number. 12in = 4.7 in 2 cm 12in = 30.4cm Should the number on the right be larger, equal, or smaller than the number on the left?
50 Assess Drill/Due Today [1 m = ft] Is the number on the right correct or should it be larger, equal, or smaller than the number on the left? 10 m = ft 10 m = 3.04 ft 5 m = 5 ft
51 Assess Drill/Due Today [1 mile = 1609 m] Which of the following is incorrect? A. 100 miles = 160 km B. 100 km = 62 miles
52 Life Science-Drill/Due Today 1. Record your height in units of feet and inches. 2. Convert your height into units of inches. 3. Convert your height from inches into units of meters.
53 Cutnell s Cover page
54 Scientific Notation Purpose: reduce large numbers to powers of tens. distance Scientific Notation Prefex centimeter meter kilometer megameter gigameter
55 Metric Prefixes Prefix Symbol Factor Giga G 10 9 Mega M 10 6 Kilo K 10 3 Centi C 10-2 Micro µ 10-6 Nano n 10-9
56 Example Convert 5 inches into nanometer m = 1nm Critical Thinking Is one inch larger than 1 nm? Would one inch equal a big number of nm or a small number of nm?
57 Example Convert 5 inches into nanometer m = 1nm 2.54cm 1m 1nm 5in in 100cm m 5in = nm
58 Life Science-Drill/Due Today Determine the diameter of a Polio virus in units of inches. Order of magnitude approximation.
59 2. Time Units of time: Seconds = s [60 s = 1 min] Minutes = min [60 min = 1 h] Hours = h [24 h = 1 day] Days [365 days = 1 yr] Years = yr
60 Moderate-Drill/Due Today Convert 1 yr into s. 1yr 365days yr 24hr days 60min hr 60s min 7 = s π 10 7 s
61 Life Science Drill/Due Today Measure your neighbor s heart rate. 1. Count the number of pulses in 10 s. 2. Calculate the number of pulses in one minute. 3. Estimate the number of your heart beats from birth to the present.
62 3. Mass Measurement of the resistance to a change in motion. Units of mass: Gram SI (Systeme International) Slug (British Engineering System) Note: mass does not have units of pound! Mass is not weight!
63 Dimensions Drill/Due Today FF = mm? If F has dimensions of (mass length/time 2 ) and m has dimensions of mass, then what are the dimensions of? A. length B. length/time C. length/time 2 D. None
64 Dimensions Drill/Due Today EE = mm? If E has dimensions of (mass length 2 /time 2 ) and m has dimensions of mass, then what are the dimensions of? A. length 2 B. length/time 2 C. length 2 /time 2 D. None
65 Brief History of Mass What is Mass? Mass is a measurement of an object s resistance to change in motion. Mass and Energy are equivalent. Mass distorts space.
66 In the News: Gravity Waves
67 Gravity Wave Detectors WA 4km LA en.wikipedia.org/wiki/ligo
68
69 Mass and Weight Confusion 131 Kg or 288 lbs
70 Mass and Weight Mass Weight
71 Dimensions Drill/Due Today Mass also can have units of: A. Pounds B. Feet C. Celsius D. None of the above
72 Physiology-Drill/Due Today Convert your weight in pounds into a weight in units of Newton (N). 1 lb = N
73 Mass On Earth: mass = weight 9.8m / (N) 2 s Example: 1 Newton weight has a mass of 1N mass = 9.8m / s 2 = 0.10kg
74 Math-Drill/Due Today Determine you mass in units of kilograms.
75 Math-Drill/Due Today Determine you mass in units of slugs. Conversion factor: 1 slug = kg
76 Multiple Units Convert 65 miles per hours into units of meters per second. 1 mi/h = m/s m mi s 65 = h mi 1 h Assess the speed using an analogy. 29 m s
77 Multiple Units What if you can t find a direct conversion factor? For example convert 60 miles per hours into inches per second. From the appendix Length Time 1 mi = 5280 ft 1 m = in = ft 1 h = 3600 s
78 Multiple Units mi 5280ft 39.37in 60 h mi 3.281ft 1h 3600s =1056 in s
79 Life Science-Drill/Due Today Suppose your hair grows at the rate of 1/32 inch per day. Find the rate at which it grows in nanometers per second.
80 Area Conversion Convert 50 m 2 into cm 2 1 m = 100 cm 2 100cm 50 m 2 1m 4 = 50m m cm 2 = cm 2
81 Architect-Drill/Due Today A house has 1000 ft 2 area. What is the area in metric units? [1 ft = m]
82 Architect-Drill/Due Today A house has 500 m 2 area. What is the area in British units? [1 ft = m]
83 Volume Conversion Convert 200 m 3 into cm 3 1 m = 100 cm 100cm 200m 3 1m = 200m 3 3 = m 8 cm 3 cm 3
84 Architect-Drill/Due Today The dimensions of a house are 10 m 20 m 5 m. Determine the volume of the house in cubic feet. [1 ft = m]
85 Architect-Drill/Due Today The dimensions of a house are 25 ft 15 ft 8 ft. Determine the volume of the house in cubic feet.
86 Assessment Drill/Due Today State if the numbers in red correct of if it should be larger, equal, or smaller than the numbers in blue. 1. The fastest humans can walk about 2 m/s. that s about 10 mph. 2. An average car is about 15 ft long. That s about 5 m. 3. The 5 minutes is roughly about 1,000 seconds.
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