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lecture2 - 1.5 Vectors and Scalars Scalars are...

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1.5 Vectors and Scalars Scalars are quantities (including units) that give the size or magnitude of something. Examples: Mass = 45 kg Length = 16.2 m Speed = 15.0 m/s Vectors are objects that require both magnitude AND direction to completely describe them. Examples: Displacement = 10 m, 20 o N of E Velocity = 25 m/s, 35 o above the horizontal Vectors are usually represented as arrows. The arrow points along the direction of the vector, and the length of the vector arrow is proportional to its magnitude. Remember Vectors have direction, scalars do not! In the book, the vectors are represented in bold face. In class and on homework, i h ld h i h b h i quizzes, etc., you should represent them with an arrow above the quantity. T For example, a tension force:
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Example: Represent a position vector r that is 10 m in length and directed at 20 o N of E. N r Vectors are extremely important!!! They occur everywhere in physics Many objects are in motion W E 20 o everywhere in physics. Many objects are in motion, moving in all directions!!! S 1.6 Vector Addition and Subtraction The simplest situation occurs when the vectors are collinear , i.e. they lie along the same direction. Example : A car moves due east with a displacement vector A = 275 m. It then continues to move due east with a displacement vector B = 125 m. What is the total displacement vector, R, of the car? What we want to find is R = A + B.
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N E A = 275 m B = 125 m R = 275 m due east + 125 m due east = 400 m due east R = 400 m Wh ddi l l h il f h d h h d f h When adding two vectors, always place the tail of the second vector on the head of the first. What if the two vectors to be added are not collinear??? Example : A car first moves with a displacement vector A = 275 m due east. It then moves with a displacement vector B = 125 m at 55 o N of W. What is the total displacement of the car? i.e. what is R = A + B.
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N Since these vectors are head to tail, the resultant vector is drawn from the origin to the head of the second vector. First, how do I find the magnitude of R , i.e. its length?
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