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Conservation of Energy
On An Inclined Plane
BlackBoard Notes

• Is the final kinetic energy of a cart sliding down a frictionless incline proportional to the vertical distance fallen?

• s_o = Photogate coordinate
• s = Starting cart coordinate
• x = | s - s_o |

     h = x sinθ

• Model: Track is nearly frictionless, so use energy conservation:
  • K_i + V_i = K_f + V_f
  • 0 + mgh = K_f + 0
  • K = mgh
  • ^K/_m = gh = gx sinθ
  • but, ^K/_m = ^1/₂mv2/_m = ^v2/₂
  • so, ^v2/₂ = g sinθ x

  So, plot ^v2/₂ vs. x.

• What type of equation do we try as a fitting function?

  (y) = m(x) + b

  (^v2/₂) = a(x) + b

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Revised: 30 Sep 2005

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