physics 170 - mechanicsmorse/p170fa15-2.pdf · vector summary 23 graphical vector addition: place...
TRANSCRIPT
Scalar and Vector QuantitiesScalar quantities are completely described by magnitude only (temperature …).
Vector quantities need both magnitude (size) and direction to completely describe them (force, displacement, velocity,…).
Represented by an arrow, the length of the arrow is proportional to the magnitude of the vector.
Head of the arrow represents the direction.
Indicated by the name with an arrow on top of it.
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Scalars Versus Vectors
How to get to the Library: you need to know how far (0.5 miles) and which way.
Need to have consistent systems of units for the measurements
Need rules for dealing with the uncertainties
Scalar: quantity is a number with units
Vector: quantity has both a magnitude (with units) and a direction
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The Components of a Vector
Even though you know how far and in which direction the library is, you may not be able to walk there in a straight line.
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Example: how high is the building?
• Known: angle and one side • Find: !another side • Key: tangent is defined via • two sides!
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• Length, angle, and components can be calculated from each other using trigonometry:
• Convention: We measure counterclockwise from the +x axis
The Components of a Vector
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The Components of a Vector
• We can resolve vector into perpendicular components using two-dimensional coordinate systems:
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Example: Height of a Cliff In Jules Vern’s Mysterious Island,
Capt. Cyrus Harding wants to find the
height of a cliff. He stands with his
back to the base of the cliff and
marches straight away from it for 500 ft.
At this point, he lies on the ground and
measures the angle from horizontal to
the top of the cliff. (a) If the angle is 34.0°, how high is the cliff?
(b) What is the straight line distance d from Capt. Harding to the top of the cliff?
Any valid physical equation must be dimensionally 10
Question 1A vector has a negative x-component and a positive y-component. The angle theta that specifies its direction is measured counterclockwise from the x axis. In what range is theta ?
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Adding Vectors Graphically
Adding vectors graphically:
Place the tail of the second at the head of the first. The sum points from the tail of the first to the head of the last.
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Subtracting Vectors
The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here, D = A – B.
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Adding Vectors by Components
• 1) Find the components of each vector to be added.
• 2) Add the x- and y-components separately.
• 3) Find the resultant vector.
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Vector Summary
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Graphical vector addition: Place tail of second at head of first; sum points from tail of first to head of last or parallelogram method placing vectors to the same origin.
Unit VectorsUnit vectors are dimensionless vectors of unit length. For example, the vector
has magnitude (with units) Ax and points along the +x axis.
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