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Physics 218 Summer 2009 Deepak K Pandey Office:Physics 87 Phone:494-3018 Email:dpandey@purdue.edu
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Today: (Ch. 1 & 2) Motion, Forces and Newton’s law Graphs Tomorrow: (Ch. 2 & 3) Force and Motion Along a Line HDisplacement, Velocity and Acceleration HNormal force and weight HFriction
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Chapter 2: Motion, Forces and Newton’s law Scalars and Vectors Forces Newton’s law of motion Net force (vector addition) Free body diagram Contact forces (tomorrow)
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Scalars and Vectors Vocabulary: Scalars are numbers Examples: 10 meters 75 kilometers/hour Vectors are numbers with a direction Example: 10 meters to the right 75 kilometers/hour north
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Scalars and Vectors Scalar: 25 meters Vector: 25 meters north Scalar: 25 meters Vector: 25 meters east
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Adding Vectors To add two vectors, A + B A B 1. place the head of one vector on the tail of the other vector B A 2. draw a new vector from the tail of the first to the head of the second B AC 3. This new vector is is called the resultant A + B = C
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Subtracting Vectors To subtract two vectors, A - B A B 1. Multiply vector B by -1: A + (-B) A -B 2. Then simply add A and -B, head to tail. -B A C 3. A + -B = C
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The Components of a Vector A = x + y We call x and y the components of the vector A. A y x O P
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Addition of Vectors (using Components) A + B = C Add the x components of A and B to each other to get the x component of C. Then, add the y components of A and B to each other to get the y component of C. Let see How do we find the x and y components? C B A
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Addition of Vectors (using Components) A A x A y B x B y B C C x C y
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Example If B has a magnitude of 25 kilometers in a direction 30 degrees North of East, what is the x component of B? B B y B x =30 o
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Example You travel 2 km due East on 26th street, then turn right on Main street and head Southeast for 1 km, what are the components of your displacement?
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Group Problem Solving If A has a magnitude of 10 meters, and is pointing 45 degrees South of East, what is the magnitude (length) of the vector A y ? AyAy A AxAx
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x0x0 Net Force: Vector addition
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x vector to final position x
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change in x displacement (change in position) x = x - x 0 xx Displacement
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change in x displacement (change in position) x = x - x 0 xx Displacement x vector to final position x x 0 vector to initial position x0x0
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Speed and Velocity Speed is a scalar: what your speedometer reads. (meters/second) Velocity is a vector: the speed, in a certain direction (meters/second at degrees) Examples: 100 meters/second 41 kilometers/hour Southwest
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Average Speed & Velocity average velocity = average speed in the specified direction
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Average Acceleration
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Example A police airplane notices that your car only took 2 seconds to travel between two white marks on the highway that are 100 meters apart. Will you get a ticket?
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Graphical Representation
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Example: Ball rolling up and down
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HW1: Dimensional Analysis Consider the equation mgh = mv 2, where m has dimensions of mass (units of kilograms), g has dimensions of length/time 2 (m/s 2 ), h has dimensions of length (meters), and v has units of length/time (m/s). a.Is this equation dimensionally correct or incorrect? b.What is the units of the combination g/v 2 ?
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HW1: Density The mass of an object is m = 26 kg, and its volume is V = 0.006 m 3. What is its density, m/V? Be sure to give the correct number of significant figures in your answer. Number of significant digits required = 1
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Tomorrow: (Ch. 2 & 3) Force and Motion Alone a Line Displacement, Velocity and Acceleration
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Addition of Vectors (using Components) A A x A y B x B y C B C x C y
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