Principles of Physics I: Projectile Motion and Circular Motion - Prof. Arthur La Porta, Study notes of Physics

Download Principles of Physics I: Projectile Motion and Circular Motion - Prof. Arthur La Porta and more Study notes Physics in PDF only on Docsity! 1 PHYS141 Principles of Physics I Prof. Arthur La Porta alaporta@umd.edu Rm 1111, IPST building (building #085) Office hours: Wed 1pm-2pm, Thurs 1pm-2pm Chapter 4 Advantages of resolution into components Derivations for motion with constant acceleration apply equally well to components of 2D or 3D motion. 2 2atvtxx if ++= j ta tvyitatvx tatvrr y yii x xii iif ˆ 2 ˆ 2 2 22 2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +++⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ++= ++= r rrr 1D equation: 2D equation: 2 Chapter 4 Simple Example: Projectile Motion An object is launched with some initial velocity. During free motion (neglecting wind resistance) particle experiences constant downward acceleration due to the gravitational pull of the earth. Value of this acceleration is 2m/s80.9−=g Vertical motion is affected by this acceleration of Horizontal motion occurs with no acceleration (constant velocity) unless some outside force is exerted on the object. However, motion is synchronized Chapter 4 Projectile motion Y motion has constant acceleration equal to –g X motion has no acceleration, constant velocity. jgttvyitatvx tatvrr yii x xii iif ˆ 2 ˆ 2 2 22 2 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − +++⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ++= ++= r rrr2D equation: 0 X and Y motion are synchronized. When one coordinate triggers an event (projectile hits the ground, etc.) the motion of the other coordinate terminates at the same time. 5 Chapter 4 Maximizing Distance of Projectile Motion 0 50 100 150 200 250 300 0 50 100 150 y (m ) x (m) 15 degrees 30 degrees 45 degrees 60 degrees 75 degrees •Shallow angle: rapid movement in x, short hang time. •Steep angle, long hang time, slow movement along x •45 degrees, best combination of hang time and movement along x Chapter 4 Projectile motion A playground is on the flat roof of a city school, 6.00m above street level. The vertical wall of the building is 7.00m high, forming a 1m high railing. A ball is thrown up from the street from a point 24.0m from the wall at an angle of 53 degrees. The ball takes 2.2 s to reach a point vertically above the wall. Find the speed at which the ball is launched Find the vertical distance by which the ball clears the wall Find the distance behind the wall where the ball lands. 6m 7m 24m 6 Chapter 4 Circular motion v2v1 Is particle accelerating? Acceleration of object undergoing circular motion? 1. To the right 2. To the left 3. Upwards 4. Downwards 5. Zero v2v1 7 Chapter 4 Circular motion v2v1 v1 v2 Δv r v t r r v t v a 2 = Δ Δ = Δ Δ = rr r r1 r2 r1 r2 Δr r rv v r r v v r r rr Δ =Δ Δ = Δ