Vectors

1
Vectors
A
B
2
Vector Definition

• Any measurement which includes both size and
  direction
• 10 m/s isnt a vector
• 25 m/s SW is a vector

3
Size and Scale

• The resultant of a vector addition can be
  measured or calculated using scale drawings or
  Pythagorean Theorem

4
Vector Addition 0º 0r 180º

• 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

5 m E
3 m E

8 m E
5 m E
3 m W

2 m E
5
Vector Addition 900

• To add vectors at 90º use a drawing or Pythagoras
  Theorem
• c ?(a2 b2)
• ?(3.02 4.02)
• 5.0 cm
• ? tan-1(E or W vector/N or S vector)
• tan-1(3.0 / 4.0)
• 37o

b 3.0 cm E
a 4.0 cm N
r 5.0 cm 37o
6
Directions

• 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
NW quadrant 360 - angle
NE quadrant just find angle
W,270 º
E,90 º
SE quadrant 180 - angle
SW quadrant 180 angle
S,180 º
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Example Problem

• 5 N S 12 N W
• 13 N SW

8
Resolving Vectors

• A vector may be resolved into 2 right angled (
  orthogonal) components. This technique can be
  used to add vectors at odd angles together.

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Example Resolve 15 m/s 235o into components
along compass axes.

• 1. Determine the quadrant
• SW
• 2. Calculate acute angle
• 55o
• 3. Calculate magnitude of components
• 15 sin55o 12 m/s W
• 15 cos55o 9 m/s S

15 m/s 235o
10
Example 2 Add 15 m/s 235o 35 m/s 3560 by
resolving into components along compass axes and
then adding components.

• 15 m/s 235o
• Acute angle 55o
• 15cos55 9 ms-1 S
• 15sin55 12ms-1 W
• 35 m/s 3560
• Acute angle 4o
• 35cos4 35 ms-1N
• 35sin4 2 ms-1 W
• Resultant
• 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

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Classwork (8 bonus pts)

• 25.5 N 129o 36.7 N 322o
• 25.5 N 129o 19.8 N E 16.0 N S
• 36.7 N 322o 22.6 N W 28.9 N N
• 28.9 N N 16.0 N S 12.9 N N
• 19.8 N E 22.6 N W 2.8 N W
• 12.9 N N 2.8 N W 13.2 N N

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Lab 7

• Your mission is to fly around the country
  (minimum 10 trips) to find a possible site for a
  SCICORP regional office.
• Come home when youre done!
• Click on map to retrieve assignment

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Scale

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

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Lab 7

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

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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 5.13 cm W
• ?(2.552 5.132)
• 5.73 cm
• Next, convert to km using scale 1 cm 250 km
• 5.73250 1 430 km
• Calculate direction (use notes)
• SW

• Now make 10 sequential trips around the country.
  (Bonus points for gt20 trips)