1. Chapter 5Projectile Motion and Satellites

2. Projectile Motion Describe the motion of an object in TWO dimensions Keep it simple by considering motion close to the surface of the earth for the time being Neglect air resistance to make it simpler

3. Projectile Motion The ball is in free fall vertically and moves at constant speed horizontally!!!

4. Projectile Motion

5. Projectile Motion

6. Projectile Motion

7. Projectile Motion

8. Projectile Motion

9. Projectile Motion y x

10. What happens when we add air resistance? Adds a new force on the ball The force is in the opposite direction to the ball’s velocity vector and is proportional to the velocity at relatively low speeds Need calculus to sort out the resulting motion Lowers the angle for maximum range Projectile Motion

11. The trick to maximum range is just to keep the object off the ground for as long as possible. This allows the horizontal motion to be a maximum since x = vxt Make range longer by going higher for your starting point Make range longer by having more velocity Projectile Motion

12. Projectile Motion

13. Curvature of the earth enters into our calculations Satellites If I start 5 m above the surface, it will still be at 5 m after one second if it is moving 8000 m/sec

14. Satellites Throw at 8000 m/sec This is about 18,000 mph Earth circumference is 25,000 miles Takes 25000/18000 = 1.4 hours = 84 minutes Higher altitude longer

15. Satellites Force of gravity on bowling ball is at 90o to velocity, so it doesn’t change the velocity!!! If no air resistance, gravity doesn’t change speed of satellite, only direction!!!

16. Farther out you go, the bigger the circumference of the orbit It takes longer for the trip Also, gravity weakens by inverse square law the farther out you go Make the distance so that it takes 24 hours for the orbit Satellite is stationary in the sky!!! Communications Satellites

17. Distance is about 240,000 miles Takes 27.3 days to make an orbit The Moon

18. Give the object a speed a bit greater than 8 km/sec and the orbit will be elliptical Elliptical Orbits

19. Elliptical Orbits

20. Elliptical Orbits Sum of distances from foci to point on the ellipse is a constant!!!

21. Each planet moves in an elliptical orbit with the sun at one focus of the ellipse. The line from the sun to any planet sweeps out equal areas of space in equal time intervals The squares of the periods of the planets are proportional to the cubes of their average distances from the sun Kepler’s Laws

22. Kepler’s Laws

23. Energy Conservation

24. Energy Conservation

25. Energy Conservation

26. Escape Speed Throw at > 11.2 km/sec and ball escapes the pull of the earth!!!