1.2 Units














The Gimli Glider Incident:
July 23, 1983, Air Canada Flight 143 ran completely out of fuel halfway through its flight from Montreal to Edmonton because the amount of fuel needed was incorrectly calculated.  

1.77 pounds/liter???   
0.8 kg/liter???

http://www.pri.org/stories/2012-02-23/new-clues-emerge-centuries-old-swedish-shipwreck


"Vasa set sail on her maiden voyage on August 10, 1628. At the time, she was the most powerfully armed warship in the world, with 64 bronze cannons.Twenty minutes into her journey, the ship was hit by two strong winds. It heeled to port, water gushed in, and the ship sank less than a mile into the journey. Thirty people died.
"We have, over the last three years, measured every single piece of the wood in the ship," says Hocker. "If we want to understand how the ship was built, that's what it takes."
Hocker's meticulous measurements paid off. They gave him fresh insight into what made the Vasa unstable.
For one thing, the ship was asymmetrical, more so than most ships of the day.

Why was the ship so lopsided?
While examining the ship, Hocker discovered four rulers the workmen had used. Those rulers were based on different standards of measurement at the time.
Two were in Swedish feet, which were divided into twelve inches. The other two were in Amsterdam feet, which had eleven inches in a foot. So each carpenter had used his own system of measurement.
"When somebody tells him, make that thing four inches thick, his four inches is not going to be the same as the next guy's four inches," says Hocker. "And you can see those variations in the timbers, as well."
 
 





What are units?

Conventions used for describing the magnitude of physical quantities.

What are Equations?
Formulas relating different physical quantities (or units) to one another.


Most equations are nothing more than unit conversion statements....

Tip:  

If the units work out correctly in your calculations, you're more than half way there.


Some unit conversion tables:









Think about the units around you, develop an intuition for the magnitudes around you.






Intuition vs. Math
What length, time, and mass scales are intuitive?
What scales follow classical Newtonian Physics?
At what scale does classical physics break down?




What can you perceive without tools of any kind - with just your bare senses?

Mass__________________________



from Greek μᾶζα (maza), meaning "barley cake, lump [of dough]" The property of a physical body which determines the body's resistance to being accelerated by a force and the strength of its mutual gravitational attraction with other bodies.




What is the largest object you can lift?

Aug 8, 2012 Behdad Salimikordasiabi, 22, won the gold medal in the men’s super-heavyweight division of weight lifting, cementing his status as the biggest sports hero in Iran.  Salimikordasiabi holds the world record in the snatch at 472 pounds (214 kg = 214,000 g).

What is the smallest mass you can detect?


One drop of water -

50 ul - 99 ul
60 ul = 0.06 grams = .0001 lbs

(one liter of water weighs a kilogram)

What is the order of magnitude of masses we are used to dealing with?








Length_______________________

Standing in one place, using only your eyes

How far can you see?

 http://www.livescience.com/33895-human-eye.html
Andromeda galaxy - 2.6 million light years from earth...
2 miles (3.22 km) away - when you start seeing headlights on a car.





What is the smallest thing you can see?
Dust in the air :
10-1000 microns = .0004 - .04 inches




After contemplating what scales humans usually operate in.... now contemplate

What scale does the universe act on?



Mass of an electron
= 9.10938291 × 10-31 kg

Plank Length = 
1.616 × 10-35 m

The speed of light = 299,792,458 meters per second = 186,000 miles/sec

Size of the universe ~ 14 billion light years

Density of observable universe ~
3 × 10-30 g/cc

Mass of observable universe ~
3 × 1055 grams










Some scales are not intuitive, and can only be partially perceived through the use of math and tools.







 

 

Puzzles of modern science:
The laws that govern the universe on the largest scale are entirely different from the ones that govern on the medium and smallest scales.






General relativity:
Applies within the largest scales




Unified description of gravity as a geometric property of space and time, or spacetime.

curvature of spacetime → →

→→energy & momentum of matter and radiation

(Predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light.)

Classical Physics:
Applies within medium scales & the rules we will be using within our statics class.


Quantum mechanics:
Applies within small nanoscopic scales, or atomic and subatomic length scales.


particle physics, nuclear physics, quantum optics...
wave-particle duality, principle of uncertainty





entanglement - "spooky action at a distance", etc.




Start thinking about the units around you....



  

Gasoline prices:
http://www.mytravelcost.com/Norway/gas-prices/
http://www.mytravelcost.com/petrol-prices/




~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Set up a unit conversion excel worksheet for use throughout the rest of the semester:
* change any of the "1.00"'s to another #, and watch what happens.



Significant Digits Review:









How to round numbers:

 http://www.wikihow.com/Round-Numbers


Test Excel - How does it round numbers?





Example Unit Conversion questions:______________________


1. The Golden Gate Bridge is 1970 m long.  What is it's length in miles to three significant digits?

2. The orbital velocity of the International Space Station is 690m/s.  Determine its velocity in km/hr and in mi/hr to three significant digits.




3. A machinist drills a circular hole in a panel with radius r = 8mm.  Determine the circumference C and area A of the hole to four significant digits in cm^2 and in^2.



4. Suppose that you have just purchased a Ferrari F355 coupe and you want to know whether you can use your set of SAE (U.S. Customary unit) wrenches to work on it.  You have wrenches with widths w = 1/4 in., 1/2 in., 3/4 in., and 1 in., and the car has nuts with dimensions n = 5mm, 10mm, 15mm, 20mm, 25mm.   Defining a wrench to fit if w is no more than 2% larger than n,  which of your wrenches can you use?






5. In December 1986, Dick Rutan and Heana Yeager flew the Voyager aircraft around the world nonstop.  They flew a distance of 40,212 km in 9 days, 3 minutes, and 44 seconds. 


(a) Determine the distance they flew in miles to three significant digits 


(b) Determine their average speed (the distance flown divided by the time required) in kilometers per hour, and knots (nautical miles per hour) to three significant digits.




6. Engineers who study shock waves sometimes express velocity in millimeters per microsecond (mm/us).  Suppose the velocity of a wavefront is measured and determined to be 5 mm/us.  Determine its velocity:


(a) in m/s


(b) in mi/s

(c) in mi/hr






7. A horsepower is 550 ft-lb/s A watt is 1 N-m/s. Determine the number of watts generated by


(a) the Wright brother's 1903 airplane,

which had a 12-horsepower engine;


(b) a modern passenger jet with a power of


100,000 horsepower at cruising speed.




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