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14 Cards in this Set
- Front
- Back
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A (1) is any positive or negative physical quantity that can be completely specified by its magnitude
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(1) Scalar
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A (1) is any physical quantity that requires both magnitude and direction for its complete description
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(1) Vector
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If a vector is multiplied by a positive scalar, its magnitude is increased by (1)
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(1) The amount multiplied
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All vectors obey the (1) law of addition
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(1) Parallelogram
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<R = A+B = B+A> is the (1) property of (2)
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(1) Commutative
(2) Addition |
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If two vectors are (1), i.e., both have the same line of action, the parallelogram law reduces to an (2) or (3) addition: (4)
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(1) Collinear
(2) Algebraic (3) Scalar (4) R = A+B |
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The difference between two vectors <A> and <B> of the same type can be expressed: (1)
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(1) <R = A-B = A + (-B)
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Law of cosines or law of sines can be used to fine the (1) and its (2). The two forces <F1> and <F2>, and the resultant vector <FR> usually create a (3) triangle
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(1) Magnitude
(2) Direction (3) Scalene |
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<F> sometimes is to be resolved into two components along the two members, defined by u and v axes. To determine the magnitude of each component, a (1) is constructed first, by drawing (2) , constructing a (3) -- which represents the (4)
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(1) Parallelogram
(2) Forces Parallel to the Axes (3) Triangle (4) Triangle Rule |
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If more than two forces are to be added, successive applications of the (1) can be carried out, in order to find the resultant; thus, <FR> = (2)
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(1) Parallelogram Law
(2) <(F1+F2) + F3> |
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Procedure for Analysis
Parallelogram Law Two "component" forces <F1> and <F2> add according to the (1), yielding a resultant force <FR> that forms the diagonal of the parallelogram |
(1) Parallelogram Law
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Procedure for Analysis
Parallelogram Law If a force <F> is to be resolved into components along two axes u and v: form a parallelogram so the sides of the parallelogram represent the (1) -- (2) and (3) |
(1) Components
(2) <Fu> and <Fv> |
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Label all known and unknown (1) and the (2) and identify the 2 unknowns as the magnitude and direction of <FR>, or the magnitudes of its (3)
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(1) Magnitudes
(2) Angles (3) Components |
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Example 2.1
Angles at corner opposites of the parallelogram are (1). The Angles of the obtuse angles can be found by the following math operation (2) |
(1) Equal
(2) (360 - 2(α)) / 2 -- where α is the one of the acute angles of the parallelogram |
