Fundamentals of Physics

1. Fundamentals of Physics Chapter 3 Motion in 2 &3 Dimensions • Moving in 2 &3 Dimensions • Position & Displacement • Average & Instantaneous Velocity • Average & Instantaneous Acceleration • Projectile Motion • Projectile Motion Analyzed • Uniform Circular Motion • Relative Motion Review & Summary Questions Exercises & Problems Physics 2111 Fundamentals of Physics

2. Position & Displacement Position Vector: A vector from a reference point (aka the origin) to the particle. The vectorgives the position of thegreen ball. Physics 2111 Fundamentals of Physics

3. Position & Displacement Displacement Vector: Consider a particle moving along a path. Physics 2111 Fundamentals of Physics

4. Average & Instantaneous Velocity Average Velocity = ratio of the displacement to the time interval: A vector in the same direction as the straight line connecting the starting point to the end point. Instantaneous Velocity = derivative of particle position wrt time: A vector that is tangent to the particle’s path at the particle’s position. Physics 2111 Fundamentals of Physics

5. Velocity Components Physics 2111 Fundamentals of Physics

6. Average & Instantaneous Acceleration 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. Acceleration of a particle need not point along the path of the particle. Physics 2111 Fundamentals of Physics

7. Projectile Motion 2-Dimensional Motion: a projectile moves in a vertical plane subject to the downward acceleration due to gravity. The particle is launched with initial velocity vo: 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 Physics 2111 Fundamentals of Physics

8. Projectile Motions Physics 2111 Fundamentals of Physics

9. Identical Vertical Motion Two balls are released simultaneously The vertical motions are identical. Physics 2111 Fundamentals of Physics

10. Projectile Motions Equations that describe Projectile Motion vx = v0x vy = - v0y Physics 2111 Fundamentals of Physics

11. Trajectory of a Projectile Particle Trajectory: parabolic path Physics 2111 Fundamentals of Physics

12. Range of a Projectile Physics 2111 Fundamentals of Physics

13. Range equation Physics 2111 Fundamentals of Physics

14. Maximum Range of a Projectile R is a maximum for q0 = 45o. Physics 2111 Fundamentals of Physics

15. Range of a Projectile Physics 2111 Fundamentals of Physics

16. Projectile Motion Applet http://physics.uwstout.edu/physapplets/virginia/www.phys.virginia.edu/classes/109n/more_stuff/applets/ProjectileMotion/enapplet.html Physics 2111 Fundamentals of Physics

17. The Ball Hits the Can Every Time! During the time-of-flight, both the projectile and the can fall the same distance, h, under the constant acceleration –g. Magnet (M) releases the can just as the projectile leaves the blow gun (G). Physics 2111 Fundamentals of Physics

18. Projectiles Physics 2111 Fundamentals of Physics

19. Object Falling from a Moving Plane h = 500m, v0 = 55 m/s At what value of f should the payload be released? released horizontally Physics 2111 Fundamentals of Physics

20. Cannon Firing at Pirate Ship • V0 cannonball = 82 m/s • Pirate ship is 560 m offshore • What q for cannonball to hit ship • Safe range for the ship? Physics 2111 Fundamentals of Physics

21. Great Zacchini The “flight of Emanuel Zacchini” over 3 ferris wheels v0 = 26.5 m/s, q0 = 530, h0 = 3.0 m Does he clear first Ferris wheel ? If hmax is above second Ferris Wheel, by how much does he clear it? Physics 2111 Fundamentals of Physics

22. Uniform Circular Motion The velocity is changing, but the speed is not. Hence, the particle is accelerating. The velocity is always tangent to the circular path. The acceleration is always directed radially inward. Centripetal Acceleration: Let’s prove this. Physics 2111 Fundamentals of Physics

23. Circular Motion Physics 2111 Fundamentals of Physics

24. Relative Motion in One Dimension “Reference Frame B moves @ constant velocity wrt Reference Frame A” Differentiate wrt time Differentiate wrt time Physics 2111 Fundamentals of Physics

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 vba relative to A. Differentiate wrt time Differentiate wrt time Observers in different reference frames that move at constant velocity relative to each other will measure the same acceleration. Physics 2111 Fundamentals of Physics

26. Relative Motion vpw = 215 km/h, q south of east vwg = 65.0 km/hr 200 E of N What is vpg and q Physics 2111 Fundamentals of Physics

27. Example y – y0 = v0 sin q0 t - ½ g t2 R = x – x0 = v0 cos q0 t Physics 2111 Fundamentals of Physics

28. Example: How fast should she be going? Physics 2111 Fundamentals of Physics

29. Example: Can He Make the Jump? v0 q0 = 0 y0 y – y0 = v0 sin q0 t - ½ g t2 t = 0.990 s y = 0 x – x0 = v0 cos q0 t x – x0 = 4.5 m He can’t make it! Physics 2111 Fundamentals of Physics