General Physics 2, Lec 6, By/ T.A. Eleyan 1 Lecture 6 Application (Gauss’s Law)
General physics I, lec 1 By: T.A.Eleyan 1 Lecture (2)
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Transcript of General physics I, lec 1 By: T.A.Eleyan 1 Lecture (2)
general physics I, lec 1 By: T.A.Eleyan
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Lecture (2)
general physics I, lec 1 By: T.A.Eleyan
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Scalars and Vectors Scalars have magnitude only. Length, time, mass, speed and volume are examples of scalars.
Vectors have magnitude and direction. The magnitude of is written | | Position, displacement, velocity, acceleration and force are examples of vector quantities.
general physics I, lec 1 By: T.A.Eleyan
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Properties of Vectors
Equality of Two Vectors
Two vectors are equal if they have the same magnitude and the same direction
Movement of vectors in a diagram
Any vector can be moved parallel to itself without being affected
general physics I, lec 1 By: T.A.Eleyan
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Negative Vectors
Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions)
Multiplication or division of a vector by a scalar results in a vector for which
)a (only the magnitude changes if the scalar is positive )b (the magnitude changes and the direction
is reversed if the scalar is negative.
general physics I, lec 1 By: T.A.Eleyan
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Adding Vectors
When adding vectors, their directions must be taken into account and units must be the same
First: Graphical Methods
Second: Algebraic Methods
general physics I, lec 1 By: T.A.Eleyan
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Adding Vectors Graphically (Triangle Method)
Continue drawing the vectors “tip-to-tail”
The resultant is drawn from the origin of A to the end of the last vector
Measure the length of R and its angle
general physics I, lec 1 By: T.A.Eleyan
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When you have many vectors, just keep repeating the process until all are included
The resultant is still drawn from the origin of the first vector to the end of the last vector
general physics I, lec 1 By: T.A.Eleyan
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Alternative Graphical Method Parallelogram Method
When you have only two vectors, you may use the Parallelogram Method
All vectors, including the resultant, are drawn from a common origin
The remaining sides of the parallelogram are sketched to determine the diagonal, R
general physics I, lec 1 By: T.A.Eleyan
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Vector Subtraction
Special case of vector addition
If A – B, then use A+(-B)
Continue with standard vector addition procedure
general physics I, lec 1 By: T.A.Eleyan
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Components of a Vector
These are the projections of the vector along the x- and y-axes
general physics I, lec 1 By: T.A.Eleyan
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The x-component of a vector is the projection along the x-axis
The y-component of a vector is the projection along the y-axis
Then,
cosxA A
sinyA A
x yA A A
x
y12y
2x A
AtanandAAA
general physics I, lec 1 By: T.A.Eleyan
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Adding Vectors Algebraically
(1)Choose a coordinate system and sketch the vectors
(2)Find the x- and y-components of all the vector
(3)Add all the x-components
This gives Rx:
xx vR
yy vR
(4)Add all the y-components
This gives Ry
general physics I, lec 1 By: T.A.Eleyan
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(5)find the magnitude of the Resultant
Use the inverse tangent function to find the direction of R:
2y
2x RRR
x
y1
R
Rtan
general physics I, lec 1 By: T.A.Eleyan
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Problem :
Problem: