Phys 2401: Lecture 1 Chapt. 1: Measurement

Transcription

1 Phys 2401: Lecture 1 Chapt. 1: Measurement Martha Casquete Physics and Geology Department

2

3 Agenda Units Conversion of Units Dimensional analysis Question/Observation of the Week Quizz

4 Introduction Brief Introduction to Physics Chapter 1 Measurements Measuring things Three basic units: Length, Mass, Time SI units Unit conversion Dimension

5 Classroom Response Systems: Clickers Clicker is required as part of the course Similar to requiring a textbook for the course Can t share with your classmate Clicker use will be integrated into the course To be used during most or all lectures/discussions Clicker questions will be worked into subject matter Some related issues ( My Clicker doesn t work, or I forgot my Clicker. )

6 How will we use the clicker? I pose questions on the slide during lecture. You answer using your clicker remote. Class results are tallied. I can display a graph with the class results on the screen. We discuss the questions and answers. This could be considered class participation. These can be recorded (e.g., for quizzes and attendance).

7 Physics Physics deals with the nature and properties of matter and energy. Its language is mathematics. Physics is based on experimental observations and quantitative measurements. The study of physics can be divided into six main areas: Classical mechanics Electromagnetism Optics Relativity Thermodynamics Quantum mechanics

8 Classical Mechanics Classical Mechanics: Theory that predicts qualitatively & quantitatively the results of experiments for objects that are NOT Too small: atoms and subatomic particles Quantum Mechanics Too fast: objects close to the speed of light Special Relativity Too dense: black holes, the early Universe General Relativity

9 Classical Mechanics Classical mechanics concerns the motion of objects that are large relative to atoms and move at speeds much slower than the speed of light

10 Chapter 1 Measurement Being quantitative in Physics requires measurements How tall is Ming Yao? How about his weight? Height: 2.29 m (7 ft 6 in) Weight: 141 kg (310 lb) Number + Unit thickness is 10. has no physical meaning Both numbers and units necessary for any meaningful physical quantities

11 Type Quantities Many things can be measured: distance, speed, energy, time, force These are related to one another: speed = distance / time Choose three quantity units: LENGTH MASS TIME Define other units in terms of these.

12 SI Unit for 3 Basic Quantities Many possible choices for units of Length, Mass, Time (e.g. Yao is 2.29 m or 7 ft 6 in) In 1960, standards bodies control and define Système Internationale (SI) unit as, LENGTH: Meter MASS: Kilogram TIME: Second

13 Fundamental Quantities and SI Units Length meter m Mass kilogram kg Time second s Electric Current ampere A Thermodynamic Temperature kelvin K Luminous Intensity candela cd Amount of Substance mole mol

14 Fundamental Quantities and SI Units Why should we care about SI units? Mars Climate Orbiter: SEPTEMBER 30, 1999 Likely Cause Of Orbiter Loss Found The peer review preliminary findings indicate that one team used English units (e.g., inches, feet and pounds) while the other used metric units for a key spacecraft operation. Full Story NASA measuring failure:

15 SI Length Unit: Meter French Revolution Definition, Meter = XY/10,000,000 1 Meter = about 3.28 ft 1 km = 1000 m, 1 cm = 1/100 m, 1 mm = 1/1000 m Current Definition of 1 Meter: the distance traveled by light in vacuum during a time of 1/299,792,458 second.

16 SI Time Unit: Second 1 Second is defined as atomic clock time taken 9,192,631,700 oscillations of the light emitted by a 133 Cs atom. Defining unit precisely is a science (important for, for example, GPS): This clock will neither gain nor lose a second in 20 million years.

17 SI Mass Unit: Kilogram 1 Kilogram the mass of a specific platinum-iridium alloy kept at International Bureau of Weights and Measures near Paris. Copies are kept in all other countries. Yao Ming is 141 kg, equivalent to weight of 141 pieces of the alloy cylinder.

18 September 4, 2008 Length, Mass, Time

19 Prefixes for SI Units 10 x Prefix Symbol 3,000 m = 3 1,000 m = m = 3 km 1,000,000,000 = 10 9 = 1G 1,000,000 = 10 6 = 1M 1,000 = 10 3 = 1k 141 kg =? g 1 GB =? b 1 MB =? b x=18 exa E 15 peta P 12 tera T 9 giga G 6 mega M 3 kilo k 2 hecto h 1 deca da

20 Prefixes for SI Units 10 x Prefix Symbol x=-1 deci d -2 centi c -3 milli m -6 micro µ -9 nano n -12 pico p -15 femto f -18 atto a s = s = s = 3 ms 0.01 = 10-2 = centi = 10-3 = milli = 10-6 = micro = 10-9 = nano = = pico = p 1 nm =? m =? cm 3 cm =? m =? mm

21 Derived Quantities and Units Multiply and divide units just like numbers Derived quantities: area, speed, volume, density Area = Length Length SI unit for area = m 2 Volume = Length Length Length SI unit for volume = m 3 Speed = Length / time SI unit for speed = m/s Density = Mass / Volume SI unit for density = kg/m 3

22 Derived Quantities and Units In 2008 Olympic Game, Usain Bolt sets world record at 9.69 s in Men s 100 m Final. What is his average speed? speed 100 m 9.69 s m s m/s

23 Other Unit System U.S. customary system: foot, slug, second Cgs system: cm, gram, second We will use SI units in this course, but it is useful to know conversions between systems. 1 mile = 1609 m = km 1 ft = m = cm 1 m = in. = ft 1 in. = m = 2.54 cm 1 lb = kg 1 oz = g 1 slug = kg 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds

24 Unit Conversion Useful Conversion factors: 1 inch 1 m 1 mile 1 mile = 2.54 cm = 3.28 ft = 5280 ft = 1.61 km

25 Unit Conversion Example: Convert miles per hour to meters per second: 1mi = 5280 ft mi 1mi 5280 ft 1m 1hr m hr hr mi 3.28ft 3600 s s 1 2 m s 1mi = 1.61 Km mi 1mi 1.61Km 1000m 1hr m hr hr 1mi 1Km 3600 s s 1 2 m s

26 Unit Conversion Example: Was Instructor Casquete speeding? On my way to Edinburg from Brownsville (Rancho Viejo), sometimes I travel at a speed of 30.0 m/s. Was I exceeding the speed limit? Put 1 s using unit conversion relations, as many times as necessary. Multiply or divide numbers and units.

27 Unit Conversion Example: Is Instructor Casquete speeding? Begin with 30.0 m/s = (30.0 m/s) 1 Since 1 mile = 1609 m, so we have 1 = 1 mile/1609 m Then m 1mile (30.0 ) ( ) s 1609m mile s mile / s Finally 2 mile 2 mile 60s s s 1min 2 mile 60min min 1hr 2 mile 60 min mile hr 67.5mile / hr

28 Dimensions, Units and Equations Quantities have dimensions: Length L, Mass M, and Time - T Quantities have units: Length m, Mass kg, Time s Quantity Area Volume Speed Acceleration Dimension [A] = L 2 [V] = L 3 [v] = L/T [a] = L/T 2 SI Units m 2 m 3 m/s m/s 2

29 Dimensional Analysis Necessary either to derive a math expression, or equation or to check its correctness. Quantities can be added/subtracted only if they have the same dimensions. The terms of both sides of an equation must have the same dimensions.

30 Dimensional Analysis This is a very important tool to check your work Provides a reality check (if dimensional analysis fails then no sense in putting in the numbers) Example When working a problem you get the answer for distance d = v t 2 ( velocity x time 2 ) Quantity on left side = L Quantity on right side = L / T x T 2 = L x T Left units and right units don t match, so answer is nonsense

31 Exercise 1 Dimensional Analysis The force (F) to keep an object moving in a circle can be described in terms of: velocity (v, dimension L / T) of the object mass (m, dimension M) radius of the circle (R, dimension L) Which of the following formulas for F could be correct? v (a) F = mvr (b) F m (c) R 2 F mv R 2 Note: Force has dimensions of ML/T 2

32 Exercise 1 Dimensional Analysis Which of the following formulas for F could be correct? Note: Force has dimensions of ML/T 2 A. B. C. F = mvr F F m mv R v R 2 2 Velocity (n, dimension L / T) Mass (m, dimension M) Radius of the circle (R, dimension L)

33 Mix Problems A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 X Kg. First find the dimensions of the density. Dimension of the density: M 3 L

34 Mix Problems Continue diameter= 2.4 x m mass = 1.67 x Kg R = 1.2 x m V 4 R 3 3 = 7.24X m x X kg m x10 17 kg m 3

35 Summary The three fundamental physical quantities of mechanics are length, mass and time, which in the SI system have the units meter (m), kilogram (kg), and second (s), respectively The method of dimensional analysis is very powerful in solving physics problems. Units in physics equations must always be consistent. Converting units is a matter of multiplying the given quantity by a fraction, with one unit in the numerator and its equivalent in the other units in the denominator. Unwanted are cancelled out in favor of the desired units.