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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
MEASUREMENTS
SPACE - LENGTH, AREA, VOLUME
MASS
TIME
TEMPERATURE
Actually Temp. is a property of
Mass and velocity (dist/time)
UNITS OF MEASUREMENT
Length:
Babylonian inch= 25 barleycorns
Foot = length of a foot, 12 inches
Yard = Henry V’s 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
UNITS OF MEASUREMENT
RADIAL
Arc-second
“
minute = 60 arc-sec ‘
degree = 60 minutes o
full circle = 360 degrees
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 yds
arpent
square foot
square yard = 3 x3 = 9 square feet
square mile = 640 acres
UNITS OF MEASUREMENT
VOLUME
ounce=3 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
tablespoon = 3 tsp,
= 1/3 oz
gill, dram
pinch, dash < 1/8 tsp
cubic inch
cubic foot= 1728 cu in
cubic yard=27 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.
UNITS OF MEASUREMENT
MASS:
Ounce
Troy ounce
pound = 16 oz
slug
ton = 2000 or 2200 lbs
hundredweight (cwt)
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
UNITS OF MEASUREMENT
TIME
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, coon’s age
UNITS OF MEASUREMENT
TEMPERATURE
Degree (fahrenheit)
0o 32o
-17o
0o
273.16
~100o F
37o
212o
C
K
H2O freezes Body Temperature.
100o
373.16
H 2O boils
UNITS OF MEASUREMENT
THE METRIC SYSTEM: SI
LENGTH
MASS
TIME
METRE KILOGRAM SECOND
centimetre
gram
TEMPERATURE
KELVIN
degree Celsius
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
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
4-DIMENSIONS
up/down; across; backwards/forwards
and time
IMAGINE
A “THREE”
DIMENSIONAL
WORLD
FLATLAND!
THE NOTION OF MOTION
DISTANCE
VELOCITY:
DISTANCE PER UNIT TIME
ACCELERATION:
CHANGE IN VELOCITY WITH TIME
FORCE = MASS X ACCELERATION
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
Galileo and Gravity
Galileo’s observations on gravity
It is not “natural” that all things come to a stop
NEWTON’S 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
MOMENTUM
• MOMENTUM IS THE PRODUCT OF
MASS AND VELOCITY
• M=m x v or M = md/t
• IN ANY SYSTEM MOMENTUM IS
CONSERVED
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
TORSION PENDULUM
mirror
screen
M
m
d
M
F=
GMm/d2
m
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.
FORCES
CONTACT
FORCES
Frictional force
tensional force
normal force
air resistance force
applied force
spring force
ACTION-AT-ADISTANCE FORCES
Gravitational force
electrical force
magnetic force
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?
POWER
Power is the rate of doing work
or the rate of using energy
P = Fd/t = mad/t
UNIT: WATT = NEWTON-METRE/SECOND
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.
SIMPLE MACHINES
INCLINED PLANE
LEVER
WHEEL AND AXLE
SCREW
PULLEY
WEDGE
Other useful machines:
gear, bevel gear, worm gear,
rack and pinion, cam-wheel,
crank and rod, chain, belt,
ratchet
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
CONSERVATION OF ENERGY
• THE TOTAL AMOUNT OF ENERGY IN
THE UNIVERSE CAN NEITHER BE
INCREASED OR DECREASED