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Centripetal Force and Gravity

Centripetal Force and Gravity. 4/27/07. Recap. v 2. s. a c =. s = r .  =. r. r. a c = r 2. v T = r .  . 2. =.  =. v 2.  t. T. F c = ma c = m. r. a T = r .  .  =. F c = ma c = mr 2.  t. Recap (UCM). Uniform Circular Motion.

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Centripetal Force and Gravity

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  1. Centripetal Force and Gravity 4/27/07

  2. Recap v2 s ac = s = r  = r r ac = r2 vT = r   2 =  = v2  t T Fc = mac = m r aT = r    = Fc = mac = mr2  t

  3. Recap (UCM) Uniform Circular Motion UCM means that  is constant Which means that…  = 0 aT = 0 |vT| = constant BUT… vT is not constant because the direction changes

  4. UCM

  5. UCM FSB

  6. UCM FSB

  7. UCM FSB FSB

  8. UCM FSB FSB

  9. UCM FSB FSB FSB

  10. UCM FSB FSB FSB

  11. UCM FSB FSB FSB FSB

  12. Vertical UCM

  13. Vertical UCM FSB

  14. Vertical UCM mg FSB What’s keeping the ball pinned up against the top?

  15. Vertical UCM mg FSB What’s keeping the ball pinned up against the top? Inertia

  16. Vertical UCM Fc is the sum of the inward forces on the ball. mg FSB Fc Fc =  F = FSB + mg

  17. Vertical UCM Fc is the sum of the inward forces on the ball. v2 Fc = mr2 = m r mg FSB Fc Fc =  F = FSB + mg

  18. Vertical UCM Fc is the sum of the inward forces on the ball. v2 Fc = mr2 = m r mg FSB v2 m = FSB + mg r Fc Fc =  F = FSB + mg

  19. Vertical UCM

  20. Vertical UCM Fc is the sum of the inward forces on the ball. FSB mg

  21. Vertical UCM Fc is the sum of the inward forces on the ball. FSB mg Fc =  F = …

  22. Vertical UCM Fc is the sum of the inward forces on the ball. FSB mg Fc =  F = FSB

  23. Vertical UCM

  24. Vertical UCM FSB

  25. Vertical UCM FSB mg

  26. Vertical UCM Fc is the sum of the inward forces on the ball. Fc =  F = FSB mg

  27. Vertical UCM Fc is the sum of the inward forces on the ball. Fc =  F = FSB FSB mg

  28. Vertical UCM Fc is the sum of the inward forces on the ball. Fc =  F = FSB - mg FSB mg

  29. Vertical UCM Fc is the sum of the inward forces on the ball. Fc =  F = FSB - mg v2 Fc = mr2 = m FSB r v2 m = FSB - mg r mg

  30. Vertical UCM Is the force of the string on the ball greater at the top or at the bottom?

  31. Vertical UCM mg Is the force of the string on the ball greater at the top or at the bottom? FSB FSB mg

  32. Vertical UCM What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

  33. Vertical UCM Happens when Fc just counters mg (I.e. FSB = 0) What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

  34. Vertical UCM Happens when Fc just counters mg (I.e. FSB = 0) What is the slowest vT the ball can have if it doesn’t fall when it reaches the top? v2 m = mg r

  35. Vertical UCM Happens when Fc just counters mg (I.e. FSB = 0) What is the slowest vT the ball can have if it doesn’t fall when it reaches the top? v2 m = mg r v2 = g r

  36. Vertical UCM Happens when Fc just counters mg (I.e. FSB = 0) What is the slowest vT the ball can have if it doesn’t fall when it reaches the top? v2 m = mg r v2 = g r v2 = rg

  37. Vertical UCM Happens when Fc just counters mg (I.e. FSB = 0) What is the slowest vT the ball can have if it doesn’t fall when it reaches the top? v2 m = mg r v2 = g r v2 = rg v = rg

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