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CH0102part2 - Key to the success in this class Time You...

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Key to the success in this class Time : You need to spend enough hours on it. Learn smartly : Study groups, office hour, etc. Practice, practice, and practice: HMWK, End-of- chapter problems Pre-lecture: Read the book before Post-lecture: Read the book (slides) after Train yourself to think scientifically and independently
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Chapter 1: Vectors VS Scalars Concept of vector (VS scalar) Vector addition Unit vector notation Components of vectors Vector addition using components Vector decomposition * Products of vectors (covered in later chapters)
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Vectors: Magnitude and Direction Vectors show magnitude and displacement, drawn as a ray. A physics vector is quantity that has both magnitude (how long/how fast, etc) and direction Confused? You won’t be the only One. Be patient and we will come back to this often If lost in a desert (forest) at P1, which quantity should you try to maximize (distance or displacement)
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Vector addition (consider your daily commuting route) Vectors may be added graphically, “head to tail.”
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Vector addition Example: A traveler hiked 1.00km north, then 2.00km to the west. What is the displacement (d) his ending position from the starting position?
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Vector addition Example: A traveler hiked 1.00km north, then 2.00km to the west. What is the displacement (d) his ending position from the starting position? d 2 = (1.00 km ) 2 +(2.00 km ) 2 d 2 = 5.00 km 2 d = 5.00 km tgf = 2.00 km 1.00 km = 2.00 f = tg - 1 (2.00) = 63.4 o
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Components of vectors Manipulating vectors graphically is insightful but difficult when striving for numeric accuracy. Vector components provide a numeric method of representation. Any vector is built from an x component and a y component (and z). Any vector may be “decomposed” into its x component using V *cos θ and its y component using V *sin θ (where θ is the angle the vector V sweeps out from 0°).
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Unit vectors—Figures Assume vectors of magnitude 1 with no units exist in each of the three standard dimensions. The x direction is termed i , the y direction is termed j , A vector is subsequently described by a scalar times each component. A = A x i + A y j = A cos θ i + A sin θ j Refer to Example 1.9. cos θ
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Vector addition Example II: A traveler hiked 5km at 37 degrees relative to the x-axis, then 10km at 53 degrees relative to the x-axis. What is the resultant Displacement? 37 o 53 o ρ d 1 ρ d 2 ρ d = ? θ x y DECOMPOSE first!
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Vector addition Example II: ρ d 1 = (5 km )cos37 o ö x +(5 km )sin37 o ö y = (4 km ) ö x +(3 km ) ö y r d 2 = (6 km ) ö x +(8 km ) ö y r d = r d 1 + r d 2 = (10 km ) ö x +(11 km ) ö y tgq = 11 km 10 km =1.1 q = tg - 1 (1.1) = 47.7 o A traveler hiked 5km at 37 degrees relative to the x-axis, then 10km at 53 degrees relative to the x-axis. What is the resultant Displacement? 37 o 53 o ρ d 1 ρ d 2 ρ d = ? θ x y
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Q1.1 A. E x = E cos β , E y = E sin β B. E x = E sin β , E y = E cos β C. E x = – E cos β , E y = – E sin β D. E x = – E sin β , E y = – E cos β E. E x = – E cos β , E y = E sin β What are the x and y –components of the vector r E ?
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A1.1 A. E x = E cos β , E y = E sin β B. E x = E sin β , E y = E cos β C. E x = – E cos β , E y = –
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