Maximum velocity at the lowest point

  1. Say that there is a car on a top of the hill and it was on a frictionless surface, explain why the maximum speed of the car would occur at the lowest point of the hill?

    In this case would you prove it through the conservstion of energy PE + KE = PE + KE?

    If so, how does this prove that Vmax occurs at the lowest point?

    Any help would be great, Thanks :)
     
  2. jcsd
  3. What can you say about PE at the top vs at the bottom? Which is higher?
     
  4. Assume that there is no PE at the top of the hill...

    What do you mean which is higher?
     

  5. PE is a relative phenomenon. U cant say that there is no PE at the top.
    if there is no PE at the top......PE at the bottom should be negative
     
  6. Oops... typo, PE = mgh and KE = 0
     
  7. hi friend

    Assume that height of the hill is 'h' m.

    now initially as the car is rest on the top of the hill.......KE is zero and PE is 'mgh'

    when the car is at the bottom of the hill the total PE at the top should be KE at the bottom........since PE at the bottom is zero

    At any point in between top and bottom....the total energy is the sum of both PE and KE.....but at the bottom the total energy is only KE so v is max at this point
     
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