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Transcript of MEASUREMENTS How exact? How many fingers? How accurate? What do you weigh? How precise? Are you...
![Page 1: MEASUREMENTS How exact? How many fingers? How accurate? What do you weigh? How precise? Are you tall? Approximation Estimation Uncertainty Orders of magnitude.](https://reader036.fdocuments.us/reader036/viewer/2022062804/56649e3a5503460f94b2c9e4/html5/thumbnails/1.jpg)
MEASUREMENTS
How exact? How many fingers?How accurate? What do you weigh?How precise? Are you tall?
ApproximationEstimationUncertainty
Orders of magnitude
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MEASUREMENTS
SPACE - LENGTH, AREA, VOLUME
MASS
TIME
TEMPERATURE
Actually Temp. is a property of Mass and velocity (dist/time)
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UNITS OF MEASUREMENT
Length: Babylonian inch= 25 barleycornsFoot = length of a foot, 12 inchesYard = Henry V’s nose to index fingerCubit = forearm, 18 inchesHand = width of palm, 4 inches?Furlong = 40 rods, 220 yds, 10 chainsChain = 22 yardsRod/Pole/Perch = 1/4 chain = 5 1/2 ydsMile (statute) = 8 furlongs, 5280 feetLeague = 3 land milesMile (naut) = 6076.11 feetFathom = 6 feetCable = 12 fathoms
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UNITS OF MEASUREMENT
RADIAL
Arc-second “minute = 60 arc-sec ‘degree = 60 minutes o
full circle = 360 degrees
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UNITS OF MEASUREMENT
AREA: Acre = one day’s ploughing= 1 furlong x 1 chain= 220 x 22 yards= 4840 square yards
square rod = 30 1/4 sq ydsarpentsquare footsquare yard = 3 x3 = 9 square feetsquare mile = 640 acres
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UNITS OF MEASUREMENT
VOLUME ounce=3 tbsp, 9 tspcup = 8 oz, 16 tbsppeck = 8 qts (dry)bushel= 2150.42 cu.in. = 4 pecks
= one man-load= 56 lbs
teaspoontablespoon = 3 tsp,
= 1/3 ozgill, drampinch, dash < 1/8 tsp
cubic inchcubic foot= 1728 cu incubic yard=27 cu ftpint = 2 cups, 16 ozquart = 2 ptsgallon = 4 qtsgal (US)=231 cu.in.barrel(US)= 31 1/2 galcord = 128 cu.ft.
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UNITS OF MEASUREMENT
MASS: OunceTroy ouncepound = 16 ozslug ton = 2000 or 2200 lbshundredweight (cwt)
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DENSITY
DENSITY = MASS per unit VOLUME
Principle of buoyancy
Hieron’s challenge to Archimedes in 250 BC
Density of gold = 19.3 gm/cc, Cu= 8.92 gm/cc
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UNITS OF MEASUREMENT
TIME blink, flash, twinkling, etc. as quick as you can say Jack Robinsonsecondminute = 60 secondshour = 60 minutesday = 24 hoursweek = 7 daysmonth= 28-31 days, Lunar month = one lunar cycle = 28 daysYear = 12 months, ~13 lunar monthsDecade = 10 yearsCentury = 10 decades, 100 yrsMillenium= 10 centuries, 1000 yrseon, era, age, lifetime, coon’s age
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UNITS OF MEASUREMENT
TEMPERATURE
Degree (fahrenheit)
F
C
K
32o
0o
273.16
212o
100o
373.16
~100o
37o
H2O freezes Body Temperature. H 2O boils
0o
-17o
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UNITS OF MEASUREMENT
THE METRIC SYSTEM: SI
LENGTH MASS TIME TEMPERATURE
METRE KILOGRAM SECOND KELVINcentimetre gram degree Celsius
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METRIC MEASURES
Metre: 1/40,000,000 of thecircumference of the earth on a longitude line through Paris
Second: 1/84600 mean solar day
Kilogram: a lump of platinum in Paris
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Metre: 1,650,763.73 wavelengths of Kr 86 emission
or: the distance light travels in a vacuum in 299,792,458 seconds
Second: 9,192,631,770 oscillations of Cs
A BIT MORE PRECISION
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4-DIMENSIONSup/down; across; backwards/forwards
and time
IMAGINE A “THREE”
DIMENSIONALWORLD
FLATLAND!
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THE NOTION OF MOTION
DISTANCE
VELOCITY: DISTANCE PER UNIT TIME
ACCELERATION: CHANGE IN VELOCITY WITH TIME
FORCE = MASS X ACCELERATION
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AN EXPERIMENT IN MOTION
APPARATUS
EXPERIMENT
REPORT
Car, odometer, watch, paper, pencil, driver, observer/recorder
Record the odometer reading every minute, on the minute, during a ride through the city, of at least 30 minutes duration.
Plot a graph of distance vs time
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Galileo and Gravity
Galileo’s observations on gravity
It is not “natural” that all things come to a stop
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NEWTON’S THREE LAWS
1. Inertia LawA body stays motionless or in motion ina straight line unless acted upon by a force.
2. Force = mass x acceleration
3. For every action there is an equal and opposite reaction
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MOMENTUM
• MOMENTUM IS THE PRODUCT OF MASS AND VELOCITY
• M=m x v or M = md/t
• IN ANY SYSTEM MOMENTUM IS CONSERVED
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Force of gravity F = GMm/d2
GRAVITY BY NEWTON
F = Gmm’/d2 where m and m’ are known masses
G = Fd2/mm’ = gravitational constant=6.67 x 10-11 m3/kg-s2
M = Fd2/Gm = mass of the earth= 6 x 10 24 kg
Known: m, d, F (= mg) Unknown: M (Mass of earth)
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TORSION PENDULUM
m
m M
M
mirrorscreen
F = GMm/d2
d
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Centre of Gravity
FOR EVERY OBJECT THERE IS A POINT WHICH CAN BE TREATED AS THE POINT ON WHICH AND FROM WHICH THE FORCE OF GRAVITY CAN BE ASSUMED TO ACT.
This point need not be within the object.
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FORCES
CONTACT FORCES
ACTION-AT-A-DISTANCE FORCES
Frictional forcetensional forcenormal forceair resistance forceapplied forcespring force
Gravitational forceelectrical forcemagnetic force
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WORK
Work is the product of force over a distance
W = F x d = mad
HOW HARD, HOW FAR YOU PUSHHOW HIGH, HOW HEAVY YOU LIFT
UNIT: JOULE = NEWTON-METRE
Did Sisyphus do any work?
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POWER
Power is the rate of doing work or the rate of using energy
P = Fd/t = mad/t
UNIT: WATT = NEWTON-METRE/SECOND
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MACHINES EMPOWER MAN
By extending the application of force over a longer distance, more work can be done with a given force, or the needed force can be reduced.
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SIMPLE MACHINES
INCLINED PLANE SCREWLEVER PULLEYWHEEL AND AXLE WEDGE
Other useful machines:gear, bevel gear, worm gear, rack and pinion, cam-wheel, crank and rod, chain, belt, ratchet
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ENERGYThe capacity to do work
Potential Energy Ep = mgh (mad)Kinetic Energy Ek = 1/2 mv2
Change in Energy is Power applied for a Time
E1-E0= Pt = (Fd/t) x t = Fd = madBut under constant acceleration d = 1/2 at2
so, E = 1/2ma2t2 = 1/2mv2
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CONSERVATION OF ENERGY
• THE TOTAL AMOUNT OF ENERGY IN THE UNIVERSE CAN NEITHER BE
INCREASED OR DECREASED