AP1200_Ch1_Mechanics-2Vect_Kinem-2008

# AP1200_Ch1_Mechanics-2Vect_Kinem-2008 - AP1200 1 Mechanics...

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1 AP1200 – 1. Mechanics Concepts AP1200 – 1. Mechanics Concepts 1.2 Vectors and kinematics 1.2 Vectors and kinematics Michel A. Van Hove Michel A. Van Hove WARNING: PRINTING THIS DOCUMENT WILL USE MUCH INK AND WILL NOT SHOW ANIMATIONS.

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2 Vectors Vectors Vectors are very useful in physics Definition: a vector quantity is a quantity that has both a magnitude and a direction in contrast, a scalar quantity has a magnitude only and no direction Examples: Vectors Scalars displacement distance velocity speed acceleration mass force time See also http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html 8
3 Question: velocity Question: velocity A car travels at 50 km/h is 50 km/h its velocity? (future questions will use PDA!) no: it is its speed You walk to the north at 5 km/h is this a velocity? yes 6

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4 Vector notation and addition Vector notation and addition Notations vectors are written in various ways: with arrow or hat: a , in bold characters: a underlined: a Magnitude of a vector: a = | a | Adding two displacements (vectors) the result is a vector sum the result is again a vector b a s b b + = i ˆ 9
5 Questions: vector addition Questions: vector addition Is a + b = b + a ? Is a + ( b + c ) = ( a + b ) + c ? Like scalar addition: a + b = b + a , a + ( b + c ) = ( a + b ) + c 8

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6 Example: airplane flying in crosswind Example: airplane flying in crosswind Wind drift: pilot can compensate by “crabbing” 8 v v v v |v ground | > or = or < |v |? |v ground | > or = or < |v |?
7 Example: landing and take-off in crosswind Example: landing and take-off in crosswind 8 See movie from http://www.flightlevel350.com/Aircraft_Boeing_747-400-Airline_Singapore_Airlines_Aviation_Video-1568.html

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8 Jet streams: riding the wind Jet streams: riding the wind 9 gray = jet streams (winds above > 60 kt ~ 111 km/h) blue arrows = winds at altitudes ~ 32000 ft ~ 9800 m green line = Great Circle arc between Hong Kong and San Francisco latest jet stream map is at http:// virga.sfsu.edu/crws/jetstream.html a flight from Hong Kong to San Francisco: - jetstreams flow eastward - eastbound flights try to “ride” the jet streams - this Pacific jet stream has a maximum speed of ~ 143 kt (knots) ~ 265 km/h
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AP1200_Ch1_Mechanics-2Vect_Kinem-2008 - AP1200 1 Mechanics...

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