Chapter 6 Projectile Motion

1. Chapter 6Projectile Motion Physics 1 (Garcia) SJSU

2. Projectiles • A projectile is any object that moves through space where the only force acting on the object is gravity. • The path that a projectile follows is called a trajectory. Physics 1 (Garcia) SJSU

3. Projectile Motion A ball thrown across the room follows an arced trajectory. Example of projectile motion, which combines horizontal and vertical motion. Physics 1 (Garcia) SJSU

4. Projectile Motion Projectile motion combines uniform horizontal motion (constant speed)with freefall vertical motion (constant acceleration. Physics 1 (Garcia) SJSU

5. Uniform Horizontal Motion 1 2 3 4 5 Equal Distances Arbitrary Rolling ball (with no friction) is an example of uniform motion. Velocity of the ball is constant so distance between “frames” (equal time between frames) is constant. Physics 1 (Garcia) SJSU

6. Accelerating Vertical Falling 1 (Release) 1 1 Falling is an example of accelerating motion. 2 4 3 Total distance from point of release increases in the ratios 1:4:9:16:25:… or 12:22:32:42:52… 3 9 Distance between frames increases as 1:3:5:7:9…. 5 16 4 7 Physics 1 (Garcia) SJSU

7. Projectile Motion 2 1 4 3 1 5 Arbitrary 3 Ball rolling off of a table combines horizontal and vertical motion. Falling starts with frame #4, vertical distances increasing as 1:3:5:7:… Horizontal distances equally spaced as with uniform motion. Frames #4 to #7 are projectile motion. 6 5 7 7 Physics 1 (Garcia) SJSU

8. Check Yourself At the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground. Which strikes the ground first? Physics 1 (Garcia) SJSU

9. Demo: Fall and Fire FALL 1 FIRE 1 1 One ball is released and falls straight down. Other ball is fired horizontally. At all times the balls are at the same height. Hit the ground at the same time. 2 2 3 3 3 5 4 4 Physics 1 (Garcia) SJSU

10. Movie: Shoot the Monkey http://www.youtube.com/watch?v=cxvsHNRXLjw

11. Distance Fallen From Table 3.3 (page 47) we know that distance fallen in one second is 5 meters. This distance fallen is the same whether falling straight down or in projectile motion. 0.5 s 5 meters 1.0 s 1.5 s Physics 1 (Garcia) SJSU

12. Projectile Motion & Curvature For initial speeds that are faster and faster, the range of the projectile is farther and farther. For very large speeds, the curvature of Earth starts to be noticeable. Physics 1 (Garcia) SJSU

13. Projectiles Launched at an Angle With no gravity, projectile would follow a straight line. Due to gravity, projectile falls beneath this line, just as if released from rest. No Gravity With Gravity Physics 1 (Garcia) SJSU

14. Parabolic Arc 4 1 3 5 Arbitrary Arbitrary 3 2 6 Up and down motion is symmetric, as shown. Frame #4 is highest point of the parabolic arc of projectile motion. 5 7 1 7 Physics 1 (Garcia) SJSU

15. Maximum Range Maximum range is at 45 degrees (when air resistance is negligible). Physics 1 (Garcia) SJSU

16. 45 degrees Demo: Trebuchet Trebuchet is a type of catapult popular in the 13th century. Warwolf Release Physics 1 (Garcia) SJSU

17. Movie: Trebuchet Contestant in annual pumpkin throwing contest, Punkin Chukin Physics 1 (Garcia) SJSU

18. Shape of the arc is changed. Object lands at steeper angle. Projectile Motion with Drag Range reduced by air resistance. Physics 1 (Garcia) SJSU

19. Earth’s Curvature Curvature of the Earth is about 5 meters over a distance of 8000 meters (which is about 5 yards over 5 miles). Physics 1 (Garcia) SJSU

20. Missing the Ground Suppose you throw a ball at a speed of 8000 m/s (about 18,000 mph). After one second, ball travels 8000 meters and falls 5 meters. In that distance, Earth curves by same amount (5 meters). If nothing stops the ball, what happens? 8000 m 5 m Curvature NOT to Scale Physics 1 (Garcia) SJSU

21. Newton’s Mountain Newton drew a similar illustration, picturing cannons firing from a tall mountain. If a cannon was powerful enough, the cannonball would orbit Earth. Physics 1 (Garcia) SJSU

22. Orbits and Centripetal Force Gravity provides the centripetal force required for a satellite to move in a circle. Physics 1 (Garcia) SJSU

23. Check Yourself Satellites orbit at least 150 km (about 100 miles) above the surface of Earth because: There is almost no gravity at that altitude? There is almost no air resistance? Physics 1 (Garcia) SJSU

24. Getting into Orbit Rocket needs to lift above the atmosphere and then fire thrusters to acquire the required orbital speed of about 8 kilometers per second. Returning to Earth, air resistance slows the spacecraft during reentry. Physics 1 (Garcia) SJSU

25. Elliptical Orbits For speeds higher than 8 km/s, the orbit is elliptical instead of circular. Physics 1 (Garcia) SJSU

26. Escape Speed If speed exceeds 11.2 km/s then object escapes Earth because gravity weakens (as object gets further away) and never slows the object enough to return it back towards Earth. Hyperbolic Circular Elliptical Physics 1 (Garcia) SJSU

27. End of Part I:Mechanics Physics 1 (Garcia) SJSU