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2009 Physics 2111 Fundamentals of Physics Chapter 3 1 Fundamentals of Physics Chapter 3 Motion in 2 &3 Dimensions 1.Moving in 2 &3 Dimensions 2.Position & Displacement 3.Average & Instantaneous Velocity 4.Average & Instantaneous Acceleration 5.Projectile Motion 6.Projectile Motion Analyzed 7.Uniform Circular Motion 8.Relative Motion Review & Summary Questions Exercises & Problems
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2009 Physics 2111 Fundamentals of Physics Chapter 3 2 Position & Displacement Position Vector: A vector from a reference point (aka the origin) to the particle. The vector gives the position of the green ball.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 3 Position & Displacement Displacement Vector: Consider a particle moving along a path.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 4 Average & Instantaneous Velocity Average Velocity = ratio of the displacement to the time interval: Instantaneous Velocity = derivative of particle position wrt time: A vector in the same direction as the straight line connecting the starting point to the end point. A vector that is tangent to the particle’s path at the particle’s position.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 5 Velocity Components
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2009 Physics 2111 Fundamentals of Physics Chapter 3 6 Average & Instantaneous Acceleration Acceleration of a particle need not point along the path of the particle. Average Acceleration = ratio of the change in velocity to the time interval: Instantaneous Acceleration = derivative of particle velocity wrt time: If the velocity of a particle changes in either magnitude or direction, the particle is subject to an acceleration.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 7 Projectile Motion The particle is launched with initial velocity v o : For a projectile, the motions in the vertical and horizontal planes are independent of each other: horizontal motion with zero acceleration vertical motion with constant downward acceleration 2-Dimensional Motion: a projectile moves in a vertical plane subject to the downward acceleration due to gravity.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 8 Projectile Motions
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2009 Physics 2111 Fundamentals of Physics Chapter 3 9 Identical Vertical Motion Two balls are released simultaneously The vertical motions are identical.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 10 Projectile Motions v x = v 0x v y = - v 0y Equations that describe Projectile Motion
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2009 Physics 2111 Fundamentals of Physics Chapter 3 11 Trajectory of a Projectile Particle Trajectory: parabolic path
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2009 Physics 2111 Fundamentals of Physics Chapter 3 12 Range of a Projectile
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2009 Physics 2111 Fundamentals of Physics Chapter 3 13 Range equation
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2009 Physics 2111 Fundamentals of Physics Chapter 3 14 Maximum Range of a Projectile R is a maximum for 0 = 45 o.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 15 Range of a Projectile
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2009 Physics 2111 Fundamentals of Physics Chapter 3 16 Projectile Motion Applet http://physics.uwstout.edu/physapplets/virginia/www.phys.vir ginia.edu/classes/109n/more_stuff/applets/ProjectileMotion/e napplet.html
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2009 Physics 2111 Fundamentals of Physics Chapter 3 17 The Ball Hits the Can Every Time! Magnet (M) releases the can just as the projectile leaves the blow gun (G). During the time-of-flight, both the projectile and the can fall the same distance, h, under the constant acceleration –g.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 18 Projectiles
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2009 Physics 2111 Fundamentals of Physics Chapter 3 19 Object Falling from a Moving Plane released horizontally h = 500m, v 0 = 55 m/s At what value of should the payload be released?
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2009 Physics 2111 Fundamentals of Physics Chapter 3 20 Cannon Firing at Pirate Ship V 0 cannonball = 82 m/s Pirate ship is 560 m offshore a)What for cannonball to hit ship b)Safe range for the ship?
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2009 Physics 2111 Fundamentals of Physics Chapter 3 21 Great Zacchini The “flight of Emanuel Zacchini” over 3 ferris wheels v 0 = 26.5 m/s, 0 = 53 0, h 0 = 3.0 m Does he clear first Ferris wheel ? If h max is above second Ferris Wheel, by how much does he clear it?
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2009 Physics 2111 Fundamentals of Physics Chapter 3 22 Uniform Circular Motion The velocity is changing, but the speed is not. Hence, the particle is accelerating. The acceleration is always directed radially inward. Centripetal Acceleration: The velocity is always tangent to the circular path. Let’s prove this.
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2009 Physics 2111 Fundamentals of Physics Chapter 3 23 Circular Motion
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2009 Physics 2111 Fundamentals of Physics Chapter 3 24 “Reference Frame B moves @ constant velocity wrt Reference Frame A” Relative Motion in One Dimension Differentiate wrt time
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2009 Physics 2111 Fundamentals of Physics Chapter 3 25 Relative Motion in 2 Dimensions Two observers watching the motion of particle P from the origins of reference frames A and B, while B moves at constant velocity v ba relative to A. Observers in different reference frames that move at constant velocity relative to each other will measure the same acceleration. Differentiate wrt time
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2009 Physics 2111 Fundamentals of Physics Chapter 3 26 Relative Motion v pw = 215 km/h, south of east v wg = 65.0 km/hr 20 0 E of N What is v pg and
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2009 Physics 2111 Fundamentals of Physics Chapter 3 27 Example y – y 0 = v 0 sin 0 t - ½ g t 2 R = x – x 0 = v 0 cos 0 t
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2009 Physics 2111 Fundamentals of Physics Chapter 3 28 Example: How fast should she be going?
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2009 Physics 2111 Fundamentals of Physics Chapter 3 29 Example: Can He Make the Jump? x – x 0 = v 0 cos 0 t y – y 0 = v 0 sin 0 t - ½ g t 2 0 = 0 v0v0 y0y0 y = 0 He can’t make it! t = 0.990 s x – x 0 = 4.5 m
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