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MEASUREMENTS

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

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MEASUREMENTS

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  1. MEASUREMENTS How exact? How many fingers? How accurate? What do you weigh? How precise? Are you tall? Approximation Estimation Uncertainty Orders of magnitude

  2. MEASUREMENTS SPACE - LENGTH, AREA, VOLUME MASS TIME TEMPERATURE Actually Temp. is a property of Mass and velocity (dist/time)

  3. 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

  4. UNITS OF MEASUREMENT RADIAL Arc-second “ minute = 60 arc-sec ‘ degree = 60 minutes o full circle = 360 degrees

  5. 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

  6. 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.

  7. UNITS OF MEASUREMENT MASS: Ounce Troy ounce pound = 16 oz slug ton = 2000 or 2200 lbs hundredweight (cwt)

  8. 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

  9. 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, coon’s age TIME

  10. UNITS OF MEASUREMENT TEMPERATURE Degree (fahrenheit) ~100o F 212o 0o 32o -17o 0o 100o 37o C 273.16 373.16 K H2O freezes Body Temperature. H 2O boils

  11. UNITS OF MEASUREMENT THE METRIC SYSTEM: SI LENGTH MASS TIME TEMPERATURE METRE KILOGRAM SECOND KELVIN centimetre gram degree Celsius

  12. 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

  13. 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

  14. 4-DIMENSIONS up/down; across; backwards/forwards and time IMAGINE A “THREE” DIMENSIONAL WORLD FLATLAND!

  15. THE NOTION OF MOTION DISTANCE VELOCITY: DISTANCE PER UNIT TIME ACCELERATION: CHANGE IN VELOCITY WITH TIME FORCE = MASS X ACCELERATION

  16. 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

  17. Galileo and Gravity Galileo’s observations on gravity It is not “natural” that all things come to a stop

  18. 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

  19. MOMENTUM • MOMENTUM IS THE PRODUCT OF MASS AND VELOCITY • M=m x v or M = md/t • IN ANY SYSTEM MOMENTUM IS CONSERVED

  20. 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

  21. TORSION PENDULUM mirror screen M m d M m F = GMm/d2

  22. 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.

  23. 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

  24. 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?

  25. POWER Power is the rate of doing work or the rate of using energy P = Fd/t = mad/t UNIT: WATT = NEWTON-METRE/SECOND

  26. 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.

  27. 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

  28. ENERGY The capacity to do work Change in Energy is Powerapplied 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

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

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