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    Vector and Scalar Quantities: Resultant. Graphical. Component

    Uploaded by

    Clark Joshua
    Vector and scalar quantities are classified based on whether they have a magnitude only or both a magnitude and direction. Displacement is a vector quantity that represents the change in an object's position and has both a magnitude and direction. Distance is a scalar quantity that represents how far an object moved without regard to direction. The displacement of a jogger who started at +4m and ended at -3m is -7m, while the distance traveled is 7m. Vectors can be represented by their x and y components or by their magnitude and angle. The resultant vector is found by adding the x and y components of two or more vectors.

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    Vector and Scalar Quantities: Resultant. Graphical. Component

    Uploaded by

    Clark Joshua
    37 views45 pages
    Vector and scalar quantities are classified based on whether they have a magnitude only or both a magnitude and direction. Displacement is a vector quantity that represents the change in an object's position and has both a magnitude and direction. Distance is a scalar quantity that represents how far an object moved without regard to direction. The displacement of a jogger who started at +4m and ended at -3m is -7m, while the distance traveled is 7m. Vectors can be represented by their x and y components or by their magnitude and angle. The resultant vector is found by adding the x and y components of two or more vectors.

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    Vector and scalar quantities are classified based on whether they have a magnitude only or both a magnitude and direction. Displacement is a vector quantity that represents the change in an object's position and has both a magnitude and direction. Distance is a scalar quantity that represents how far an object moved without regard to direction. The displacement of a jogger who started at +4m and ended at -3m is -7m, while the distance traveled is 7m. Vectors can be represented by their x and y components or by their magnitude and angle. The resultant vector is found by adding the x and y components of two or more vectors.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    37 views45 pages

    Vector and Scalar Quantities: Resultant. Graphical. Component

    Uploaded by

    Clark Joshua
    Vector and scalar quantities are classified based on whether they have a magnitude only or both a magnitude and direction. Displacement is a vector quantity that represents the change in an object's position and has both a magnitude and direction. Distance is a scalar quantity that represents how far an object moved without regard to direction. The displacement of a jogger who started at +4m and ended at -3m is -7m, while the distance traveled is 7m. Vectors can be represented by their x and y components or by their magnitude and angle. The resultant vector is found by adding the x and y components of two or more vectors.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 45

    Vector and

    Scalar Quantities
    Resultant. Graphical. Component.
    Physical quantities are classified
    into two:
    Scalar is a physical quantity
    that has only magnitude.
    Vector is a physical quantity
    that has both magnitude
    and direction.
     MAGNITUDE - the meaning of
    magnitude is 'size' or 'quantity’
     DIRECTION - It simply means that the
    vector is directed from one place to
    another.
    Displacement (∆d)
    A change in position,
     

    which has both


    magnitude and
    direction.
    DISPLACEMENT S

    ∆ 𝑑 =𝑑 2 −𝑑 1
     
    Obtain the displacement of a jogger
    who started at +4m and ended at
    -3m.
     
    DISTANCE:

     
    Distance (d)
    It is a scalar quantity in which direction is not specified.
     

    If the displacement from position -3 m to +4 m is -7


    m. The distance traveled is 7 m.

    =-7 m [S]; d= 7 m
    DISTANCE DISPLACEMENT
     Scalar Vectors
    Measure how far It depends on the
    we moved. sign
    Always positive It can be ( - , +)
    Direction ( -
    means left, +
    means right)
    Examples
    INITIAL FINAL
    1m 5m

    4m 2m

    -2m 3m
    VECTORS
    TWO WAYS TO REPRESENT A
    VECTOR

     X and Y components
     Magnitude and Angle
    Components of a Vector

    The word component


    means part. Hence, the
    components of a vector
    means the parts of the a
    vector. A vector has an x-
    part and a y-part.
    Solving for Components of a
    Vector
    Given a set of axes (x, y)
    where a force vector of
    316 N has a direction of
    35° North of East.

    Determine the x-part,


    which is adjacent side of
    the right triangle.
    Solving for Components of a
    Vector
    Using trigonometric
     

    function, we can use the


    acronym SOH-CAH-TOA in
    finding the x-part.
    Solving for Components of a Vector

    Since x-part is an adjacent


     

    side of the triangle and 316


    N is hypotenuse, we will use
    the cosine function
    Solving for Components of a
    Vector
    Solving for x:
     

    259 N
    Solving for Components of a
    Vector
    Determine the y-part using
     

    the 316 N and the given


    angle:

    259 N
    Solving for Components of a
    Vector
    Solving for y:
     

    181 N

    259 N
    Example # 2

    d= 10 m

     
    30
    Example # 3
    d= 18 m

     
    25
    Example # 4
    d= 18 m
     
    124
    Example # 4
    F= 10 N

     
    60
    MAGNITUDE AND direction
    (ANGLE)
    FORMULA:
     Magnitude

    v x y

     Angle
    = (y component / x component)
    EXAMPLE 1

    Fy= 3N

    Fx= 4N
    EXAMPLE 2

    Fy= 3N

    Fx= 3N
    EXAMPLE 3

    Fy= 6N

    Fx= -6N
    EXAMPLE 4

    Fy= 2N

    Fx= -3N
    EXAMPLE 5

    Fx= 2N

    Fy= -4N
    EXAMPLE 6

    Fx= 2N

    Fy= -6N
    RESULTANT VECTOR

    The resultant is the


    vector sum of two or
    more vectors.
    EXAMPLE 1
    Ay= 2N
    VECTOR A

    Ax= 6N

    By= 4N
    VECTOR B

    Bx= 4N
    EXAMPLE 2

    Determine the
    resultant vector of
    the following given;
    A= 10 m, 102 º (Q2)
    B= 5 m, 83 º (Q1)
    EXAMPLE 3

    Determine the
    resultant vector of
    the following given;
    A= 100 N , 0º
    B=150 N, 30 º
    “I am nothing, then you
    came and gave me
    direction” – Vector

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