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Classical Mechanics Lecture 10

Midterm 2 this Friday November 8 (units 4-9). Classical Mechanics Lecture 10. Today’s Concept: Center of Mass Finding it Using it. Main Points. Main Points. Center of Mass. Center of Mass. Two-Particle System. Two-Particle System. Two-Particle System. Two-Particle System.

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Classical Mechanics Lecture 10

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  1. Midterm 2 this Friday November 8 (units 4-9) Classical Mechanics Lecture 10 Today’s Concept: Center of Mass Finding it Using it

  2. Main Points

  3. Main Points

  4. Center of Mass

  5. Center of Mass

  6. Two-Particle System

  7. Two-Particle System

  8. Two-Particle System

  9. Two-Particle System

  10. Two-Particle System

  11. Two-Particle System

  12. Rigid Body: Balance Point

  13. Discrete N-body System

  14. Discrete N-body System: Example

  15. Discrete N-body System:Example

  16. Continuous Mass Distribution: Example A uniform stick of length L and mass M. dm x=L x=0

  17. Clicker Question

  18. Continuous Mass Distribution “Calculus comes to the rescue!!”

  19. Continuous Mass Distribution

  20. Continuous Mass Distribution

  21. Continuous Mass Distribution

  22. Continuous Mass Distribution

  23. Continuous Mass Distribution

  24. Center of Mass for System of Objects

  25. Center of Mass for System of Objects

  26. Center of Mass for System of Objects

  27. Finding Center of Mass: Summary

  28. Checkpoint The yummy doughnut is round and has equal weight distribution all over the doughnut, therefore, the center of mass must be in the middle A yummy glazed doughnut is shown below. Where is the center of mass of this fantastic culinary delight? A) In the center of the hole. B) Anywhere along the blue dashed line going throughthe solid part of the dough. C) The center of mass is not defined in cases where there is missing mass. x

  29. Clicker Question The disk shown in Case1 clearly has its CM at the center. Suppose the disk is cut in half and the pieces arranged as shown in Case2 In which case is the center of mass highest? A) Case 1 B) Case 2 C) same x xCM Case1 Case2

  30. Clicker Question The disk shown in Case1 clearly has its CM at the center. Suppose the disk is cut in half and the pieces arranged as shown in Case2 In which case is the center of mass highest? A) Case 1 B) Case 2 C) same x x x xCM x Case1 Case2

  31. Dynamics of the Center of Mass

  32. Dynamics of the Center of Mass

  33. Dynamics of the Center of Mass The acceleration of the center of mass of the object is determined only by the external forces

  34. Dynamics of the Center of Mass If the total (net) external force is zero, the CM won’t accelerate

  35. Clicker Question

  36. Center of Mass Equation

  37. Center of Mass Equation

  38. Center of Mass Equation Macroscopic work by friction determines motion of center of mass of the box Microscopic work at interface determines additional thermal energy in the box and the floor

  39. No Jet pack?

  40. But I have a wrench!

  41. Center of Mass stays put…

  42. Example

  43. Man on Boat

  44. Man on Boat

  45. Man on Boat Let d be the distance the boat moves to the left. The man’s new position Man is L-d.

  46. Man on Boat

  47. Man on Boat The boat’s new position in L/2-d.

  48. Homework Problem = 0.975 m =-1 m

  49. Homework Problem

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