MEASUREMENTS

How exact? How many fingers?How accurate? What do you weigh?How precise? Are you tall?

ApproximationEstimationUncertainty

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 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

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 ydsarpentsquare footsquare yard = 3 x3 = 9 square feetsquare mile = 640 acres

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.

UNITS OF MEASUREMENT

MASS: OunceTroy ouncepound = 16 ozslug ton = 2000 or 2200 lbshundredweight (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 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

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

UNITS OF MEASUREMENT

THE METRIC SYSTEM: SI

LENGTH MASS TIME TEMPERATURE

METRE KILOGRAM SECOND KELVINcentimetre gram degree Celsius

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

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

4-DIMENSIONSup/down; across; backwards/forwards

and time

IMAGINE A “THREE”

DIMENSIONALWORLD

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

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

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 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

MOMENTUM

• MOMENTUM IS THE PRODUCT OF MASS AND VELOCITY

• M=m x v or M = md/t

• IN ANY SYSTEM MOMENTUM IS CONSERVED

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)

TORSION PENDULUM

m

m M

M

mirrorscreen

F = GMm/d2

d

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

ACTION-AT-A-DISTANCE FORCES

Frictional forcetensional forcenormal forceair resistance forceapplied forcespring force

Gravitational forceelectrical forcemagnetic force

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?

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 SCREWLEVER PULLEYWHEEL AND AXLE WEDGE

Other useful machines:gear, bevel gear, worm gear, rack and pinion, cam-wheel, crank and rod, chain, belt, ratchet

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

CONSERVATION OF ENERGY

• THE TOTAL AMOUNT OF ENERGY IN THE UNIVERSE CAN NEITHER BE

INCREASED OR DECREASED