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Unformatted text preview: F e w P o in t s
! M o v i e “ P o w e r s o f t e n ” a t t h e e n d o f t h e le c t u r e ( i f t i m e ) ! N o c la s s o n M o n d a y : L a b o r d a y ! H om ew ork
• First set opened • Due by Wednesday 23:59 Physics for Scientists & Engineers 1
Fall Semester 2006
Lecture 4 ! H e lp r o o m s t a r t s o n T u e s d a y ! H o n o r s o p t i o n : la s t c h a n c e t o e n r o ll o r c h a n g e t h e h o u r s i n t h e h e lp r o o m August 29, 2006 Physics for Scientists&Engineers 1 1 August 29, 2006 Physics for Scientists&Engineers 1 2 S c ie n t ific N o t a t io n
! Physical quantities consist of a number that specifies its magnitude AND its unit
• Example: this lecture lasts 50 minutes (number) (unit) • • • • S ig n ific a n t F ig u r e s
! Two statements:
The population of the USA is 294,109,799 August 2004 The population of the USA is 294,000,000=2.94·108 First statement implies precision that is simply not warranted Second statement claims that the population is somewhere between 293M and 295M. This is justified!
US Census Bureau ! For very large or very small numbers, we use scientific notation number = mantissa ! 10 exponent
3.2x10-12) ! General Rule:
• The number of digits we write down in a number specifies the precision with which we claim to know that number. • Example: (or • Product easy: (4.8x10-17)x(7.21x107)=34.6x10-10=3.46x10-9 • You can enter number in scientific notation into the LONCAPA homework system as 3.2e-12 or 3.2*10^-12
August 29, 2006 Physics for Scientists&Engineers 1 3 3.2·10-12 August 29, 2006 Physics for Scientists&Engineers 1 4 E x a m p le : S ig n ific a n t F ig u r e s
• Suppose we are told that the radius of a circle is 2.66 feet; what is its circumference? • Formula: C = 2! r • Type 2 ! " ! 2.66 into your pocket calculator and get: S ig n ific a n t F ig u r e s - R u le s
! The number 1.62 has 3 significant digits; 1.6 has 2 significant digits. ! If you give a number as an integer, then you specify it with infinite precision. ! Leading zeros do not count for our significant digits. 0.000162 (3 sd) ! Trailing zeros do count. 1.62000 (6 sd) ! Numbers in scientific notation have as many significant digits as their mantissa. How big the exponent is has no influence. ! You can never have more significant figures than you start with in any of the factors of a multiplication or division. ! You can only add or subtract when there are significant figures for that place in every number. Example: 1.23 + 3.4461 = 4.68, and not 4.6761
5 August 29, 2006 Physics for Scientists&Engineers 1 6 16.7132729170977 • But if we only know that the radius of the circle is between 2.65 and 2.67 feet, i.e. to 3-digit precision, then we cannot claim that we know the circumference of the same circle to better than 3 digits. • It follows that we need to round our answer to 3 digits, the same precision to which we were given the initial input. • Final answer: the circumference is 16.7 feet. August 29, 2006 Physics for Scientists&Engineers 1 U n it s - T h e M e t r ic S y s t e m
! International system of units (SI) D e fin it io n o f B a s e U n it s
! 1 kilogram of mass kept in Paris is deﬁned as the mass of the international prototype of the kilogram. ! 1 second is the time interval in which 9,192,631,770 oscillations of the wave that corresponds to the transition between the two hyperﬁne states of the ground state of the cesium-133 atom take place. ! 1 meter is the length that a light beam in vacuum travels in a fraction of 1/299,792,458 of a second.
7 August 29, 2006 Physics for Scientists&Engineers 1 8 Unit Mete r kilogram Second Amp e r e Kelvin Mole candela Abbreviation m kg s A K mol cd Base unit for length ma s s time current temperatu r e amount o f a substanc e luminous intensity ! MKSA system ! Based on powers of 10 of base units ! All other units derive from these 7 units (Area: m2)
August 29, 2006 Physics for Scientists&Engineers 1 P o w e r s o f T e n P r e fix e s
10 24 10 21 1018 1015 1012 10 9 10 6 10 3 10 2 101
August 29, 2006 U n it C o n v e r s io n
y z a f p n µ m c d
9 yotta zetta exa peta te r a gig a me g a kilo hecto deka Y Z E P T G M k h da 10 !24 10 !21
!18 10 !15 10 !12 10 !9 10 !6 10 !3 10 !2 10 !1 yocto zepto atto femto pico nano micro milli centi deci ! In this class, metric units are required ! Need to know conversion factors between British and metric units
Metri c 1 cm 1 cm 1m 1 km Metri c 1g 1 kg 1 kg
August 29, 2006 = = = = = = = Bri t i s h 0.39370079 in 0.0328084 ft 3.28084 ft 0.621371 mile Bri t i s h 0.035274 oz 2.204623 lb 0.001102 ton Bri t i s h 1 in 1 ft 1 ft 1 mile Bri t i s h 1 oz 1 lb 1 ton = = = = Metri c 2.54 cm 30.48 cm 0.3048 m 1.609344 km Metri c 28.349523 g 0.453592 kg 907.18474 kg
10 = = Physics for Scientists&Engineers 1 Physics for Scientists&Engineers 1 A r e a a n d V o lu m e
Metri c 1 m2 1 km2 1 km2 = = = Bri t i s h 10.76391 sqft 0.386102 mile2 247.10538 acre Bri t i s h 1 sqft 1 mile2 1 acre = = Metri c 0.092903 m2 2.589988 km2 2147.483647 m2 M e t r o lo g y
! Research on precisions measurement ! Atomic clocks accurate to 10-15 (= 1 s in 30 million years) ! Precision needed for global positioning system ! Main US research institute: National Institute for Standards and Technology
• A ttr a c tiv e c a r e e r o p tio n fo r p h y s ic is ts • URL: Volume
Metri c 1 cm3 1 m3 1 lite r = = = Bri t i s h 0.061024 in3 35.314667 ft3 0.264172 gallon Bri t i s h 1 in3 1 f t3 1 gallon = = Metri c 16.387064 cm3 0.028317 m3 3.785412 liter Cesium Fountain Atomic Clock at NIST http://www.nist.gov/public_affairs/labs2.htm August 29, 2006 Physics for Scientists&Engineers 1 11 August 29, 2006 Physics for Scientists&Engineers 1 12 L e n g t h S c a le s
! ! ! ! Radius of atomic nucleus ~1 fm = 10-15 m Radius of atom ~1 Å = 10-10 m Radius of Earth = 6380 km Distance Earth-Sun: M a s s S c a le s 1 au = 1.495 98 ! 1011 m
! Distance to next star: 4 ly ! Size of Universe 1.5·1010 light years 1 light year= 9.46 ! 1015 m me = 9.1 ! 10 "31 kg M Earth = 6.0 ! 10 24 kg M Sun = 1.99 ! 10 30 kg m p = 1.67 ! 10 "27 kg Cover 41 orders of magnitude
August 29, 2006 Physics for Scientists&Engineers 1 13 Mass of entire Universe ~ 1051 kg August 29, 2006 Physics for Scientists&Engineers 1 14 G e n e r a l P r o b le m S o lv in g S t r a t e g ie s
1. Read the problem carefully. Ask yourself what quantities are known, what quantities are unknown, and what quantities are asked for in the solution. Write down these quantities and represent them with their commonly used symbolic letters. 2. Convert into SI units, if needed. 3. Make a sketch. 4. Find formulas that connect the known and the unknown quantities to each other. 5. Simplify your result algebraically as much as possible. 6. Put in the numbers and get to work with the pocket calculator. 7. Look at the number of significant figures and round appropriately. (Usually you should not round in intermediate steps.) 8. Judge if the answer seems realistic.
August 29, 2006 Physics for Scientists&Engineers 1 15 E x a m p le 1 .1
! Question: 13 What is the volume of a cylinder of height 4 16 inches and 3 circumference 8 16 inches? ! Answer:
• Convert to SI units
13 h = 4 16 inch=4.8125 inch Example =(4.8125 inch) ! (2.54 cm/inch) =12.22375 cm c=20.79625 cm 8
• Lets call the volume • Produce a sketch.
August 29, 2006 V and the radius r Physics for Scientists&Engineers 1 16 E x a m p le 1 .1 - c o n t .
! Find the volume of the cylinder in terms of its height and its circumference: V = ! r 2 h ; c = 2! r ! Combine and simplify: c = 2! r " r = c ! Question: R a t io s , E x a m p le 1 .2
If you increase the radius of a cylinder by a factor of 2.73, by what factor does the volume change? Assume that the height of the cylinder stays the same. 2! ch #c& V = ! r 2h = ! % ( h = ! Pocket calculator: $ 2! ' 4!
2 2 ! Answer: Example Example • Volume of a cylinder: V = ! r 2 h • Write it down formally for two different radii:
V ! r 2h " r % • Divide equations by each other: 2 = 22 = $ 2 ' V1 ! r1 h # r1 & • Insert numbers: r2 = 2.73 r1
2 2 V1 = ! r12 h V2 = ! r22 h
2 (20.8 cm)2 ! (12.2 cm) V= = 420.026447 cm 3 4" ! Rounded to three signiﬁcant ﬁgures: V = 420. cm 3
! Last step: check if this is reasonable.
August 29, 2006 Physics for Scientists&Engineers 1 ! 2.73 r1 $ V2 ! r2 $ = =# = 2.732 = 7.4529 ' V2 = 7.4529V1 V1 # r1 & "% " r1 & %
17 August 29, 2006 Physics for Scientists&Engineers 1 18 ...
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