1. Summer 2013 PHYS 218: General Physics Lecture 8: More 2D Crap… Just Kidding Read: Ch. 5.1 – 5.3

2. Something moving horizontally Free body diagram

3. The point is x and y are completely decoupled here. The x-direction follows constant velocity, regardless of the fact that the ball is falling. Similarly, the object moves in y-direction just as it would had it been simply dropped.

5. How to solve a 2D problem: First draw picture  Then break into x and y components v Write down what you know and want Choose equation v x = v cos  Solve v y = v sin 

6. Question An object is fired from a cannon with an initial speed of 100 m/s at an angle of 30 o. After 3 seconds has it hit the ground? A. Yes B.No  

7. Shoot the Monkey You fire the cannon. The monkey sees the flash and lets go to avoid the cannon ball. What angle should you set to hit the monkey? A.  

8. Why? In the absence of gravity, the monkey would hang there and the ball would follow the straight trajectory. Adding gravity to this causes both the monkey and the ball to accelerate at exactly the same rate. 

9. More violent physics You want to shoot the cannon as far as possible (to avoid the other guy’s guns). What  should you use? 

10. Trade-off between loft and forward velocity  deg  deg Lots of loft No forward velocity Lots of forward velocity no loft

11. Use independence of x and y  x lands x-component is easy. No forces means constant velocity

12. Use independence of x and y  x lands t is found by figuring out how long it would take the initial v y to become -v y.

13. Putting it together  x lands

14. Easiest way to find maximum  x lands

15. The red curve is the drag-free case. What would the trajectory look like with same initial angle and velocity but in the presence of air drag?

17. Reference Frames Important for settling arguments. Newton’s Laws gives consistent results when applied from any reference frame moving at constant velocity.

18. You can put the origin of the coordinate system at any location and Newton’s Laws still work A ball drops from a desk at a height of 3 m. What is the time required to reach the ground? 3 m3 m Origin on desk y x y x Origin on floor Either way Newton’s Laws predict same t

19. Newton’s Laws even work with an origin moving at constant velocity 70 mph 60 mph On ground 30 mph (b) Acceleration of Cheetah as viewed on truck (a) Acceleration of Cheetah viewed on ground On truck y x y x

20. Reference Frames In any inertial reference frame you agree on accelerations and therefore forces present. inertial reference frame: a reference frame moving at constant velocity

22. Quiz You are flying a 1957 Cessna 172 (top speed 150 mph) from Corpus Cristi to Minneapolis. Winds are easterly at 30 mph. Ballpark an appropriate heading. A.W B.WNW C.NNW D.N N S E W Corpus Christi Minneapolis

23. For Next Time Read Chapter 5.1-5.3

25. Quiz 5 (Prelude to circular motion) You peg the speedometer at constant speed 70 mph and whizz around a curved on-ramp. Are you accelerating? A. Yes B. No

26. You peg the speedometer at constant speed 70 mph and whizz around a curved on-ramp. Are you accelerating? A. Yes B. No y x v x ~ 0 v y ~ v v x ~ -v v y ~ 0 Quiz 5 (Prelude to circular motion)

27. You peg the speedometer at constant speed 70 mph and whizz around a curved on-ramp. Are you accelerating? A. Yes B. No y x v x ~ 0 v y ~ v Quiz 5 (Prelude to circular motion) v x ~ -v v y ~ 0 A change in direction produces an acceleration. That’s why you feel a force when you drive around a curve.