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Published byJudith Grindle Modified over 2 years ago

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Basic Physics

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Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI, METRIC, ENGLISH

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VECTOR AND SCALAR Scalar is a quantity which only signifies its magnitude without its direction. (+ / - ) Ex. 1kg of apple, 273 degrees centigrade, etc. Vector is a quantity with magnitude and direction. (+ / - ) Ex. Velocity of a moving object – a car with a velocity of 100 km/hr due to North West, etc.

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VECTOR AND SCALAR Writing conformity F Bold font F Italic font signifying its magnitude F Normal Font with an arrow head on top of it (Use this)

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VECTOR AND SCALAR Defining a Vector by: 1.Cartesian Vector Ex. F = 59i + 59j + 29k N the magnitude is F = ( ) F = N Due to which is the vector ??

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VECTOR AND SCALAR X (i) Z(k) Y(j) F = 59i + 59j + 29kN O

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VECTOR AND SCALAR Defining a Vector by: 2.Unit Vector Ex. F = F u (use the previous example) = F for magnitude (F 2 = F x 2 + F y 2 + F z 2 ) u for direction (dimensionless and unity) u F F

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VECTOR AND SCALAR Magnitude F = ( ) F = N Direction = = 0.67i j k = cos = (angle from x-axis) = cos = (angle from y-axis) = cos = (angle from z-axis) 59i + 59j + 29k u u

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VECTOR AND SCALAR X (i) Z (k) Y (j) F = N U F U = 0.67i j k = = = O

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VECTOR AND SCALAR Defining a Vector by: 3.Position Vector Similar to unit vector, it differs on how to locate the vector’s direction which is using the point coordinate. Ex. F = F u (see next example) r (position vector) r(position vector magnitude) u =

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VECTOR AND SCALAR U 6 m 4 m 2 m Given: F = 150 N Required: a. F ? b. , , ? X (i) Z (k) Y (j) F O A

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VECTOR AND SCALAR Solution: r r u = F = F u = 2i + 4j + 6k 7.48 =0.27i j +0.80k u

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VECTOR AND SCALAR Solution: F = F u = 150 (0.27i j +0.80k) F = 40.5i j + 120k = cos = (angle from x-axis) = cos = (angle from y-axis) = cos = (angle from z-axis) a. b.

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VECTOR AND SCALAR Operations of Vector 1.Addition 2.Subtraction 3.Dot Product 4.Cross Product

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VECTOR AND SCALAR 1.Addition F1F1 R F2F2 R = F1F1 F2F2 + R = (F 1 x + F 2 x) i + (F 1 y + F 2 y) j + (F 1 z+F 2 z) k = RyRy RxRx Tan -1 O

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VECTOR AND SCALAR 1.Addition F1F1 R F2F2 R = F1F1 F2F2 + R = (F 1 x + F 2 x) i + (F 1 y + F 2 y) j + (F 1 z+F 2 z) k = RyRy RxRx Tan -1 O Resultant is directed from initial tail towards final arrow head

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VECTOR AND SCALAR 2.Subtraction F1F1 R F2F2 R = F1F1 F2F2 - R = (F 1 x - F 2 x) i + (F 1 y - F 2 y) j + (F 1 z - F 2 z) k = RyRy RxRx Tan -1 O

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VECTOR AND SCALAR 2.Subtraction F1F1 R F2F2 R = F1F1 F2F2 - R = (F 1 x - F 2 x) i + (F 1 y - F 2 y) j + (F 1 z - F 2 z) k = RyRy RxRx Tan -1 O Take note and watch out !!! (the sense is opposite to the given diagram)

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VECTOR AND SCALAR 3.Dot Product F d X (i) Z (k) Y (j) F

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VECTOR AND SCALAR A. B = AB cos (General Formula) VectorMagnitude The angle between vectors (between their tails) Cartesian Unit vector dot product i. i = 1 i. j = 0i. k = 0k. j = 0 j. j = 1k. k = 1

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VECTOR AND SCALAR From Example: F. d = Fd cos (Using Vectors’ magnitude) = (F x i + F y j + F z k). (d x i + d y j + d z k) = F x d x + F y d y + F z d z (Using Component Vector) The dot product of two vectors is called scalar product since the result is a scalar and not a vector

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The dot product is used to determine: 1.The angle between the tails of the vectors. VECTOR AND SCALAR = cos -1 A. B AB 2. The projected component of a vector V onto an axis defined by its unit vector u

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Welcome to the Jungle

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VECTOR AND SCALAR X (i) Z (k) Y (j) O B A C F = 100 N Given : Figure 1 Required: 1. 2.F BA (Magnitude) Fig.1 Example:

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VECTOR AND SCALAR Solution : 1.Angle Find position vectors from B to A and B to C r BA = -200i – 200j + 100k r BC = -0i – 300j + 100k= – 300j + 100k cos = r BA. r BC r BA r BC = (300)(316.23) = =0.738 = Cos = o (answer)

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VECTOR AND SCALAR Solution : = r BA u BA = r BA 2.F BA -200i – 200j + 100k 300 = i – 0.667j k r BC u BC = r BC = -0i – 300j + 100k = – 0.949j k F BC = F BC. u BC = 100. (– 0.949j k)= -94.9j k F BA = F BC. u BA = (-94.9i j).(-0.667i – 0.667j k) = = 73.8 N(answer)

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VECTOR AND SCALAR Solution : Alternative Solution F BA = (100 N) (cos o ) = N F BA = F BA u BA = (-0.667i j k) = -49.2i – 49.2j k

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VECTOR AND SCALAR 4.Cross Product B A F X (i) Z (k) Y (j) O

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VECTOR AND SCALAR A = B x CA is equal to B cross C Apply the right hand rule i jk i x j = k j x k = i k x i = j j x i = -k k x j = -i i x k = -j i x i = 0 j x j = 0 k x k = 0 + -

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VECTOR AND SCALAR Right Hand Rule

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VECTOR AND SCALAR Right Hand Rule

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VECTOR AND SCALAR Right Hand Rule

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VECTOR AND SCALAR Right Hand Rule ……. (answer for yourself)

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VECTOR AND SCALAR A = B x C = (B x i + B y j + B z k) x (C x i + C y j + C z k) ijkBxByBzCxCyCzijkBxByBzCxCyCz = = (B y C z – B z C y )i + (B z C y – B x C z )j + (B x C y – B y C x )zA ijkBxByBzCxCyCzijkBxByBzCxCyCz = ijBxByCxCyijBxByCxCy +- = (B y C z – B z C y )i – (B x C z – B z C x )j + (B x C y – B y C x )z

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VECTOR AND SCALAR A = B x C = (B x i + B y j + B z k) x (C x i + C y j + C z k) ijkBxByBzCxCyCzijkBxByBzCxCyCz = = (B y C z – B z C y )i + (B z C y – B x C z )j + (B x C y – B y C x )zA ijkBxByBzCxCyCzijkBxByBzCxCyCz = ijBxByCxCyijBxByCxCy +- = (B y C z – B z C y )i – (B x C z – B z C x )j + (B x C y – B y C x )z Full caution for the +/- sign and subscripts

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VECTOR AND SCALAR Example: Given : Figure 2 Required : 1.M o (Moment at point O) 2.M y (Moment about y axis) B A F = 100N X (i) Z (k) Y (j) O MoMo

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VECTOR AND SCALAR Solution: Finding the vectors needed F= F u = i – 250j – 200k ( ) () F= 78.07i – 48.79j – 39.04k OA= 400j OB= 400i + 150j – 200k

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VECTOR AND SCALAR B A F = 100 N X (i) Z (k) Y (j) O MoMo 400j 400i + 150j – 200k F= 78.07i – 48.79j – 39.04k

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VECTOR AND SCALAR MoMo = = MoMo = i – 31228kN.mm FOA x i jk MoMo = N.mm = cos -1 (-0.447) = (angle from x-axis) = cos -1 0 = (angle from y-axis) = cos = (angle from z-axis)

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VECTOR AND SCALAR MoMo = MoMo = i – 31228kN.mm FOB x MoMo = N.mm = cos -1 (-0.447) = (angle from x-axis) = cos -1 0 = (angle from y-axis) = cos = (angle from z-axis) i jk =

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