1. Physics 7B Lecture 903-Mar-2010 Slide 1 of 19 Physics 7B-1 (A/B) Professor Cebra Kinematics Winter 2010 Lecture 9

2. Physics 7B Lecture 903-Mar-2010 Slide 2 of 19 1 st Law: The velocity of an object will not change unless acted upon by a force 2 nd Law: The net force on an object is equal to the rate of change of momentum 3 rd Law: For every force there is an equal but opposite force Newton’s Laws of Motion

3. Physics 7B Lecture 903-Mar-2010 Slide 3 of 19 Newton’s First Law -- Statics Long Range Forces Act on the center of gravity 1)Gravitational Force 2)Electrical Force Contact Forces Act the point of contact Consider every point of Contact 1)Normal Forces (Perpendicular to Surface) Can take any value needed 2)Frictional Forces (Parallel to surface) Can take any value up to  s N Dynamic friction =  D N No Motion or Constant Motion Do sample problems here

4. Physics 7B Lecture 903-Mar-2010 Slide 4 of 19 Newton’s First Law -- Statics

5. Physics 7B Lecture 903-Mar-2010 Slide 5 of 19

6. Physics 7B Lecture 903-Mar-2010 Slide 6 of 19 Newton’s Second Law -- Dynamics F R F v When do we use force/torque? When do we use impulse? Talk about vectors

7. Physics 7B Lecture 903-Mar-2010 Slide 7 of 19 Constant Acceleration Rotational Motion (  = constant) Linear Motion (a = constant)  0 +  t v = v 0 + at  = (1/2)(  0 +  )t y = (1/2)(v 0 + v)t  =  0  0 t + (1/2)  t 2 y = y 0 + v 0 t + (1/2)at 2  2 =  0 2 + 2  v 2 = v 0 2 + 2ay

8. Physics 7B Lecture 903-Mar-2010 Slide 8 of 19 Applying the Kinematics Equations 1)Make a drawing to represent the system being studied 2)Decide which directions will be called positive and which negative 3)In an organized way, write down the values for any of the kinematic variables (x, y, v, a, t and initial values). Be alert for the implied meaning in the phrasing of the problem. For example, the phrase “starts at rest” implies that v 0 = 0. 4)Determine which equation will provide the required answer using the information given.

9. Physics 7B Lecture 903-Mar-2010 Slide 9 of 19 Demo: Ball Drop Independence of Directions mg VxVx y = y 0 + v y0 t + (1/2)a y t 2 x = x 0 + v x0 t + (1/2)a x t 2 F = mg = ma y

10. Physics 7B Lecture 903-Mar-2010 Slide 10 of 19 The Monkey Hunter The monkey drops from the tree the moment that the rifle is fired. Where should one aim to hit the monkey as it falls?

11. Physics 7B Lecture 903-Mar-2010 Slide 11 of 19 The Monkey Hunter  arctan(h/x) x h t = x/(v cos  r ) v y m = h + v y0 t + (1/2)gt 2 y b = 0 + v sin  r t + (1/2)gt 2 y b = y m  h = vt sin  r sin  r = (h/vt) = (h/x)cos  r tan  r = h/x DEMO: Monkey Hunter

12. Physics 7B Lecture 903-Mar-2010 Slide 12 of 19 Maximum Trajectory Demo: Water Rockets A projectile will follow a parabolic trajectory. Which firing angle will travel the furthest? Flight time: y = y 0 + v y0 t + (1/2)a y t 2  0 = 0 + v sin  t – (1/2)gt 2  t = (2v/g) sin  Distance traveled: x = x 0 + v x0 t + (1/2)a x t 2  x = 0 + v cos  t + 0 x = v 2 2sin  cos  /g x = v 2 sin(2  )/g Maximum range when  =45

13. Physics 7B Lecture 903-Mar-2010 Slide 13 of 19 Rolling Bodies mg  Normal Force: F N = mg cos  Parallel Force: F P = mg sin  Frictional Force: f <  s F N  s mg cos  Angular Acceleration  = I   = fR Linear Acceleration F tot = ma F tot = mg sin  – f  = a/R

14. Physics 7B Lecture 903-Mar-2010 Slide 14 of 19 Inclined Planes Linear motion: s = 0 + v 0 t – (1/2) ((mg sin  - f)/m) t 2 Demo: Inclined Planes Which will go higher? A hoop or a frictionless puck? Consider conservation of energy

15. Physics 7B Lecture 903-Mar-2010 Slide 15 of 19 Rotating Projectiles A body can rotate about a fixed pivot point. A free body rotates about it center of gravity DEMO: Center of Gravity

16. Physics 7B Lecture 903-Mar-2010 Slide 16 of 19 Center of Gravity The center of gravity (or Center of mass) is the point about which an object will rotate. For a body under goes both linear projectile motion and rotational motion, the location of the center of mass will behave as a free projectile, while the extended body rotates around the c.o.m. Parabolic trajectory of the center of mass Extended body rotating with constant angular velocity

17. Physics 7B Lecture 903-Mar-2010 Slide 17 of 19 Center of Gravity Angular impulse Parabolic trajectory of the center of mass

18. Physics 7B Lecture 903-Mar-2010 Slide 18 of 19 Rotating Off Axis

19. Physics 7B Lecture 903-Mar-2010 Slide 19 of 19 Pendulum System θ F gravity F tension θ

20. Physics 7B Lecture 903-Mar-2010 Slide 20 of 19 Announcements Final Exam RoomLast Name Begins With: 198 YoungN - Z 1100 Social SciencesC - M 55 RoesslerA - B The final exam will be Wednesday March 17 th 3:30 – 5:30 Bring a student ID with picture

21. Physics 7B Lecture 903-Mar-2010 Slide 21 of 19 DL Sections

22. Physics 7B Lecture 903-Mar-2010 Slide 22 of 19

23. Physics 7B Lecture 903-Mar-2010 Slide 23 of 19