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PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 2:

PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 2: Chapter 2 – Motion in one dimension Time and Position Time and Velocity Time and Acceleration Special relationships for constant acceleration. Some updates/announcements. iclicker exercises:

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PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 2:

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  1. PHY 113 C General Physics I • 11 AM – 12:15 PM TR Olin 101 • Plan for Lecture 2: • Chapter 2 – Motion in one dimension • Time and Position • Time and Velocity • Time and Acceleration • Special relationships for constant acceleration PHY 113 C Fall 2012 -- Lecture 2

  2. Some updates/announcements PHY 113 C Fall 2012 -- Lecture 2

  3. iclicker exercises: Webassign Experiences so far Have not tried it Cannot login Can login Have logged in and have completed one or more example problems. Textbook Experiences Have no textbook (yet) Have complete physical textbook Have electronic version of textbook Textbook is on order Other PHY 113 C Fall 2012 -- Lecture 2

  4. Comment on Webassign #1 problem: 7. A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16%, its mass increases by 16.8 kg. Find the lamb's mass at the end of this process. • Problem solving steps • Visualize problem – labeling variables • Determine which basic physical principle(s) apply • Write down the appropriate equations using the variables defined in step 1. Check whether you have the correct amount of information to solve the problem (same number of knowns and unknowns). Solve the equations. Check whether your answer makes sense (units, order of magnitude, etc.). PHY 113 C Fall 2012 -- Lecture 2

  5. 7. A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16%, its mass increases by 16.8 kg. Find the lamb's mass at the end of this process. L PHY 113 C Fall 2012 -- Lecture 2

  6. i>clicker exercise: What did you learn from this problem? It is a bad idea to have a pet lamb This was a very hard question I hope this problem will not be on an exam My physics instructor is VERY mean All of the above. PHY 113 C Fall 2012 -- Lecture 2

  7. Motion in one-dimension PHY 113 C Fall 2012 -- Lecture 2

  8. Graphical representation of position (displacement) x(t) t (s) PHY 113 C Fall 2012 -- Lecture 2

  9. Comment: Your text mentions the notion of a “scalar quantity” in contrast to a “vector quantity” which will be introduced in Chapter 3. In most contexts, a scalar quantity – like one-dimensional distance or displacement can be positive or negative. Another comment: Your text describes the time rate of change of displacement as “velocity” which, in one-dimension is a signed scalar quantity. In general “speed” is the magnitude of velocity – a positive scalar quantity. PHY 113 C Fall 2012 -- Lecture 2

  10. Graphical representation of position (displacement): x(t)  time rate of change of displacement = velocity: v(t) t (s) PHY 113 C Fall 2012 -- Lecture 2

  11. Instantaneous velocity vB vC vA vD vE vF t (s) PHY 113 C Fall 2012 -- Lecture 2

  12. Demonstration of tangent line limit PHY 113 C Fall 2012 -- Lecture 2

  13. Average velocity versus instantaneous velocity PHY 113 C Fall 2012 -- Lecture 2

  14. Average velocity iclicker exercise: This results is: Exact Approximate PHY 113 C Fall 2012 -- Lecture 2

  15. Webassign Example PHY 113 C Fall 2012 -- Lecture 2

  16. Instantaneous velocity using calculus x v PHY 113 C Fall 2012 -- Lecture 2

  17. Anti-derivative relationship x t PHY 113 C Fall 2012 -- Lecture 2

  18. Velocity PHY 113 C Fall 2012 -- Lecture 2

  19. Acceleration PHY 113 C Fall 2012 -- Lecture 2

  20. Rate of acceleration • iclickerexercise • How many derivatives of position are useful for describing motion: • 1 (dx/dt) • 2 (d2x/dt2) • 3 (dx3/dt3) • 4 (dx4/dt4) •  PHY 113 C Fall 2012 -- Lecture 2

  21. Anti-derivative relationship PHY 113 C Fall 2012 -- Lecture 2

  22. Examples v(t) x(t) PHY 113 C Fall 2012 -- Lecture 2

  23. Examples v(t) x(t) PHY 113 C Fall 2012 -- Lecture 2

  24. Summary PHY 113 C Fall 2012 -- Lecture 2

  25. Another example x(t) v(t) PHY 113 C Fall 2012 -- Lecture 2

  26. From webassign: PHY 113 C Fall 2012 -- Lecture 2

  27. Another example (m/s) (s) PHY 113 C Fall 2012 -- Lecture 2

  28. Another example -- continued (m/s) (s) PHY 113 C Fall 2012 -- Lecture 2

  29. Special relationships between t,x,v,a for constant a: PHY 113 C Fall 2012 -- Lecture 2

  30. Special relationships between t,x,v,a for constant a: PHY 113 C Fall 2012 -- Lecture 2

  31. Special case: constant velocity due to earth’s gravity In this case, the “one” dimension is the vertical direction with “up” chosen as positive: a = -g = -9.8 m/s2 y(t) = y0 + v0t – ½ gt2 y0 = 0 v0 = 20 m/s At what time tm will the ball hit the ground ym= -50m ? Solve: ym = y0 + v0tm – ½ gtm2 quadratic equation physical solution: tm = 5.83 s PHY 113 C Fall 2012 -- Lecture 2

  32. Helpful mathematical relationships (see Appendix B of your text) PHY 113 C Fall 2012 -- Lecture 2

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