Vectors AB Vector Definition l Any measurement which includes both size and direction l 10 m/s isn’t a vector l 25 m/s [SW] is a vector.

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Presentation transcript:

Vectors AB

Vector Definition l Any measurement which includes both size and direction l 10 m/s isn’t a vector l 25 m/s [SW] is a vector

Size and Scale l The resultant of a vector addition can be measured or calculated using scale drawings or Pythagorean Theorem

Vector Addition [0º 0r 180º] l Two vectors pointing in the same direction are simply added [direction same] Two vectors pointing in opposite directions are simply subtracted [direction of larger vector] m [E] 3 m [E] = 8 m [E] 5 m [E] 3 m [W] = 2 m [E]

Vector Addition [90 0 ] l To add vectors at 90º use a drawing or Pythagoras Theorem l c =  (a 2 +b 2 ) l =  ( ) l = 5.0 cm l  = tan -1 (E or W vector/N or S vector) l = tan -1 (3.0 / 4.0) l =37 o r = 5.0 cm [37 o ] a = 4.0 cm [N] b = 3.0 cm [E]

Directions l Use the compass rose to the left to calculate the direction of a vector. Find angle and then transform it according to quadrant. N,0º E,90 º S,180 º W,270 º NE quadrant: just find angle SE quadrant: angle SW quadrant: angle NW quadrant: angle

Example Problem l 5 N [S] + 12 N [W] = l 13 N [SW]

Resolving Vectors l A vector may be “resolved” into 2 right – angled ( orthogonal) components. This technique can be used to add vectors at odd angles together.

Example: Resolve 15 m/s [235 o ] into components along compass axes. l 1. Determine the quadrant SW l 2. Calculate acute angle 55 o l 3. Calculate magnitude of components 15 sin55 o = 12 m/s [W] 15 cos55 o = 9 m/s [S] 15 m/s [235 o ] 9 m/s [S] 12 m/s [W]  =55 0

Example 2: Add 15 m/s [235 o ] + 35 m/s [356 0 ] by resolving into components along compass axes and then adding components. l 15 m/s [235 o ] l Acute angle = 55 o l 15cos55 = 9 ms -1 [S] l 15sin55 = 12ms -1 [W] l 35 m/s [356 0 ] l Acute angle = 4 o l 35cos4 = 35 ms -1 [N] l 35sin4 = 2 ms -1 [W] l Resultant l =12 ms -1 [W] + 9 ms -1 [S] + 35 ms -1 [N] + 2 ms -1 [W] = 14 m/s [W] + 26 m/s [N] = 30 m/s [NW] 55 o 4o4o

Classwork (8 bonus pts): l 25.5 N [129 o ] N [322 o ] = 25.5 N [129 o ] = 19.8 N [E] N [S] 36.7 N [322 o ] = 22.6 N [W] N [N] 28.9 N [N] N [S] = 12.9 N [N] 19.8 N [E] N [W] = 2.8 N [W] 12.9 N [N] N [W] = 13.2 N [N]

Lab # 7 l Your mission is to “fly” around the country (minimum 10 trips) to find a possible site for a SCICORP regional office. l Come home when you’re done! l Click on map to retrieve assignment

Scale l On the map, the scale indicates that 2.02 cm = 500 km l This means that 1 cm = _____ km l 250 km

Lab 7 l Log your flights using the lab 7 word document in the physics assignments folder l Compile the itinerary underneath the map

First Trip: DC to Little Rock Draw vector from DC to Little Rock. Find size by right clicking on it and choosing “format auto-shape” 2.55 cm [S] cm [W] =  ( ) = 5.73 cm Next, convert to km using scale 1 cm = 250 km = 5.73*250 = km Calculate direction (use notes) SW Now make 10 sequential trips around the country. (Bonus points for >20 trips)