Chapter 4 Notes-Vectors
First, a short Review:
• Scalar-Magnitude only
• Vector-Magnitude & Direction
• Some vectors: Velocity, Acceleration, Forces
• How do we draw forces?
With VECTORS
Vectors
• The magnitude of a vector is always POSITIVE
• The direction of a vector can be positive or negative.
• Directions of vectors are usually defined as North, South, East, West
• An arrow is used to depict a vector.
• The arrow’s length represents the magnitude of the vector.
• The arrow points in the Direction of the magnitude
Types of Vectors
• Force Vectors
-we use these to draw all the forces acting on an object
• Velocity Vectors
-we use these to draw the direction and speed of objects
• Weight Vectors
-we use these to draw how gravity is pulling down on an object
Parts of a Vector
• Components-single vectors when there are 2 or more
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Resultant Vector-one vector that has the same effect as the combination of the
others
What do we do to get the ―New Vector‖ when we have 2 vectors going in the same
direction
ADD their magnitudes
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What do we do to get the ―New Vector‖ when we have 2 vectors going in opposite
directions
SUBTRACT their magnitudes
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This ―New Vector‖ is the Net Vector
or RESULTANT
The resultant vector is the actual displacement
• 2 Displacement Vectors are equal when they have the same length and direction,
even if they start and end in different places.
• Because of this we can MOVE vectors to add and subtract them.
• Remember—
The Tail to Tip Method
Tail to Tip or
• Another way to put vectors together is the parallelogram method.
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Used when can’t use tail to tip.
Parallelogram Method
• Parallelogram – 4 sided shape in which the opposite sides are parallel and equal in
length
• The RESULTANT is the diagonal of the parallelogram
Again, the resultant is the diagonal of the parallelogram
• If you measure the length of the diagonal you have the magnitude of the resultant
• Example 1-See Overhead pics
Weight Vectors
• Weight--- has to do with gravity
• So a weight vector is always drawn 90 degrees from the middle of the object that has
the weight
• See overhead pictures
Velocity Vectors
• Very important Term----Relative---Means ―in relation to‖
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Example, ―relative to the ground‖ or ―relative to someone standing on the ground‖
or ―relative to someone on the bus‖
Bus examples
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A few more velocity vector terms:
Headwind-means wind head on, so that the object is moving against the direction,
opposite
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Tailwind-means wind from behind or moving in the same direction as the object
Air plane pilots can’t expect to reach their destination by simply using directions.
They must take into account the plane’s velocity relative to the air and the air’s
velocity relative to the ground.
You can then get the velocity of the plane to the ground.
This tells the pilot how fast then plane must travel relative to the ground to reach its
destination.
Say a plane is trying to travel due north at a certain speed, but the wind is blowing south east at a
certain speed.
The pilot must know how to add vectors to know how the plane will travel “relative to the
ground”
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Motorboat head due east at 11 m/s relative to the water across a river that flows due north
at 5 m/s. What’s the velocity of the motor boat with respect to the shore?
• If two sides are known, you could use
A2 + B2 = C2
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If an angle is given, we use the parallelogram method to draw the picture and
trig functions to calculate the sides(components)
Example 2-See overhead, we will revisit this soon
Resolution of Vectors
• How do you resolve the vectors?
• It’s called the resolution of vectors.
• Determine the components and solve for the sides when the resultant has been given
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See overhead pics 2 & 3
Draw the proper direction to represent the diagonal given. Then the vertical (y) and
horizontal (x) lines are drawn at the tail of the given vector so that a
rectangle/parallelogram is drawn that encloses the vector given.
Example 3-on overhead again
Equilibrium Vectors-Net Force Acting on a system equal zero
Example 4-See overhead pics
Vectors same direction-Add
Vectors opposite direction-Subtract
Vectors @ 90 degrees- Draw a Parallelogram (might separate into 2 triangles)
Pythagorean or Trig Functions to get the components and or resultant