MEASUREMENTS

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MEASUREMENTS
How exact? How many fingers? How accurate?
What do you weigh? How precise? Are you tall?
Approximation Estimation Uncertainty 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 barleycorns Foot length of
a foot, 12 inches Yard Henry Vs nose to index
finger Cubit forearm, 18 inches Hand width of
palm, 4 inches? Furlong 40 rods, 220 yds, 10
chains Chain 22 yards Rod/Pole/Perch 1/4
chain 5 1/2 yds Mile (statute) 8 furlongs,
5280 feet League 3 land miles Mile (naut)
6076.11 feet Fathom 6 feet Cable 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 days ploughing 1 furlong x 1
chain 220 x 22 yards 4840 square
yards square rod 30 1/4 sq yds arpent square
foot square yard 3 x3 9 square feet square
mile 640 acres
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UNITS OF MEASUREMENT
VOLUME
ounce3 tbsp, 9 tsp cup 8 oz, 16 tbsp peck 8
qts (dry) bushel 2150.42 cu.in. 4
pecks one man-load 56 lbs teaspoon tablespoo
n 3 tsp, 1/3 oz gill, dram pinch, dash
lt 1/8 tsp
cubic inch cubic foot 1728 cu in cubic yard27
cu ft pint 2 cups, 16 oz quart 2 pts gallon
4 qts gal (US)231 cu.in. barrel(US) 31 1/2
gal cord 128 cu.ft.
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UNITS OF MEASUREMENT
MASS
Ounce Troy ounce pound 16 oz slug ton 2000
or 2200 lbs hundredweight (cwt)
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DENSITY
DENSITY MASS per unit VOLUME
Principle of buoyancy
Hierons 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
blink, flash, twinkling, etc. as quick as you
can say Jack Robinson second minute 60
seconds hour 60 minutes day 24 hours week 7
days month 28-31 days, Lunar month one lunar
cycle 28 days Year 12 months, 13 lunar
months Decade 10 years Century 10 decades,
100 yrs Millenium 10 centuries, 1000 yrs eon,
era, age, lifetime, coons age
TIME
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UNITS OF MEASUREMENT
TEMPERATURE
Degree (fahrenheit)
F
212o
100o
32o
0o
-17o
0o
100o
37o
C
273.16
373.16
K
H2O freezes Body Temperature. H
2O boils
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UNITS OF MEASUREMENT
THE METRIC SYSTEM SI
LENGTH MASS TIME
TEMPERATURE METRE KILOGRAM SECOND
KELVIN centimetre gram degree
Celsius
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METRIC MEASURES
Metre 1/40,000,000 of the circumference 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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A BIT MORE PRECISION
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
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4-DIMENSIONS up/down across backwards/forwards
and time
IMAGINE A THREE DIMENSIONAL WORLD
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
Car, odometer, watch, paper, pencil, driver,
observer/recorder
EXPERIMENT
Record the odometer reading every minute, on the
minute, during a ride through the city, of at
least 30 minutes duration.
REPORT
Plot a graph of distance vs time
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Galileo and Gravity
Galileos observations on gravity
It is not natural that all things come to a stop
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NEWTONS THREE LAWS
1. Inertia Law A body stays motionless or in
motion in a 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
• Mm x v or M md/t
• IN ANY SYSTEM MOMENTUM IS CONSERVED

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GRAVITY BY NEWTON
Force of gravity F GMm/d2
Known m, d, F ( mg)
Unknown M (Mass of earth)
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
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TORSION PENDULUM
mirror
screen
M
m
d
M
m
F GMm/d2
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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
ACTION-AT-A-DISTANCE FORCES
CONTACT FORCES
Gravitational force electrical force magnetic
force
Frictional force tensional force normal force air
resistance force applied force spring 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 PUSH HOW 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 SCREW LEVER PULLEY WHEEL 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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ENERGY The capacity to do work
Change in Energy is Power applied for a
Time E1-E0 Pt (Fd/t) x t Fd mad But under
constant acceleration d 1/2 at2 so, E
1/2ma2t2 1/2mv2
Potential Energy Ep mgh (mad) Kinetic Energy
Ek 1/2 mv2
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CONSERVATION OF ENERGY

• THE TOTAL AMOUNT OF ENERGY IN THE UNIVERSE CAN
  NEITHER BE INCREASED OR DECREASED