Topic 1 2D Motion PHYSICS 231 Current Assignments Homework Set 1 due this Thursday Jan 20 11 pm Homework Set 2 due Thursday Jan 27 11pm Reading Chapter 4 5 for next week 01 14 2019 Physics 231 Spring 2011 2 Key Concepts 2D motion Vector Displacement Velocity and Acceleration are vectors Representations Graphical angle and magnitude components Add subtract vectors Decompose in components and add components to obtain total vector Treat 2D motion as 2 separate problems one for xdirection and one for y direction decompose all vectors in x and y components 01 14 2019 Physics 231 Spring 2011 3 Clicker Quiz What is a vector A A set of coordinates B A quantity that has a magnitude and a direction C A pointer that indicates a direction D An arrow 01 14 2019 Physics 231 Spring 2011 4 Clicker Quiz If A is a vector Ax denotes A The x component B The magnitude in x direction C The length D The magnitude of the vector 01 14 2019 Physics 231 Spring 2011 5 Vector Concept A vector is a quantity that has a direction and a magnitude Examples so far displacement velocity and acceleration In 1D the direction was given by the sign and a coordinate axis direction In 2D its more complicated Different representations can be used 01 14 2019 Physics 231 Spring 2011 6 Representation Graphical Graphically as arrow Direction is direction of arrow Magnitude is length of arrow need to define some scale Note where one draws the arrow is irrelevant Addition by adding arrows form a chain Subtraction by adding a inverted arrow 01 14 2019 Physics 231 Spring 2011 7 Clicker Quiz Which 2 vectors are the same A B C D They are all different vectors 01 14 2019 Physics 231 Spring 2011 8 Vector addition subtraction River water velocity Vr Vb vb vr 01 14 2019 Physics 231 Spring 2011 Velocity of boat relative to the water 9 Checking Understanding Which of the vectors below best represents the vector sum P Q Slide 3 16 Checking Understanding Which of the vectors below best represents the difference P Q Slide 3 18 Checking Understanding Which of the vectors below best represents the difference Q P Slide 3 20 Representation Components Components A Ax Ay Magnitudes Ax and Ay are called x and y components y A Ax Ay Parallel to y axis Parallel to x axis X Calculate components for given A Ax A cosQ Ay A sinQ Calculate magnitude of A if components are given A Ax2 Ay2 01 14 2019 Physics 231 Spring 2011 13 Checking Understanding What are the x and y components of these vectors A B C D E 3 2 2 3 3 2 2 3 3 2 Slide 3 23 Checking Understanding What are the x and y components of these vectors A B C D E 3 2 2 3 3 4 1 1 4 4 Slide 3 23 Checking Understanding What are the x and y components of these vectors A B C D E 3 1 3 4 3 3 4 3 3 4 Slide 3 25 2D Motion Treat as two separate 1D problems with time as the common parameter In X direction calculate with x components v x t v 0x ax t 1 2 x t x 0 v 0x t ax t 2 In Y direction calculate with y components v y t v 0y ay t 01 14 2019 1 2 y t y 0 v 0y t ay t 2 Physics 231 Spring 2011 17 Vector algebra graphical Addition A B C add beginning of B to end of A C points then from beginning of A to end of B Negative vector B A B has opposite direction of A but same magnitude flip arrow Subtraction A B C is same as A B C flip direction of B then add Multiply with scalar s B A s direction stays the same multiply length with s for s 0 flip direction 01 14 2019 Physics 231 Spring 2011 18 Vector algebra components In component notation things become simple Addition add components Subtraction subtract components Multiply with scalar multiply each component 01 14 2019 Physics 231 Spring 2011 19 Clicker Quiz A cart is moving along a track when a ball is vertically launched off the moving cart Will the ball A hit the track behind the cart B hit the cart C hit the track ahead of the cart 01 14 2019 Physics 231 Spring 2011 20 Clicker quiz A spring mechanism on a moving to the right cart gives a ball an upward velocity Which best represents the vector of the initial velocity of the ball just when it leaves the spring Vertical y Horizontal x A 01 14 2019 Vertical y Horizontal x B Vertical y Horizontal x C Physics 231 Spring 2011 Vertical y Horizontal x D 21 Clicker Quiz The gun barrel is straight and aligned with the aim of the gun The monkey is hanging on the tree but will let go exactly at the moment the bullet leaves the gun Where does the hunter need to aim the gun at in order to hit the monkey A A bit above the monkey B Right at the monkey C A bit below the monkey 01 14 2019 Physics 231 Spring 2011 22
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