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Roller Coaster Question

  1. Jun 10, 2009 #1
    1. The problem statement, all variables and given/known data
    A 4.0X104 (or 40,000) Kg roller coaster starts from rest at point A. Neglecting friction, calculate its potential energy relative to the ground, its kinetic energy and speed at points B, C, and D.

    http://img189.imageshack.us/img189/6162/1234q.png [Broken]
    (scanned Image, if you can't see the first number its 54 m)
    The answers are given =
    Point B:
    Ek = 1.5x107 J
    Eg = 5.9x106 J
    V = 28 m/s
    Point C:
    Ek = 2.4x106 J
    Eg = 1.8x107 J
    V = 11 m/s
    Point D:
    Ek = 7.2x106 J
    Eg = 1.4x107 J
    V = 19 m/s

    2. Relevant equations
    Gravitational Potential Energy = Mass X Gravity X Hight or Eg= M X g X h
    Kinetic Energy = 1/2 MV2 or Ek= 0.5 X M X V2
    Total Energy = Gravitational Potential Energy + Kinetic Energy Or ET= Eg + Ek



    3. The attempt at a solution
    OK so i got Point B right
    But the problem is point C

    Point A: is the Total energy so to get it
    Eg= 40,000 X 9.81 X 54
    Ek = 0 Because its at rest
    Et= Eg + Ek
    Et = 21189600

    Point B:
    Eg= 40,000 X 9.81 X 15
    Eg= 5886000 Or 5.9x106 Which is the answer they gave us
    Ek= 21189600 - 5886000
    Ek= 15303600 or 1.5x107 Which is also the right answer
    Ek= 1/2 MV2
    15303600=(0.50)(40,000) V2
    765.18 = V2
    27.6 = V or 28 Which is the right answer

    Point C:
    Eg= 40,000 X 9.81 X 47
    Eg= 18442800 or 1.8x106 Which is the right answer
    Ek= ET - Eg
    Ek= 21189600 - 18442800
    Ek= 2746800 or 2.7x106 Which is WRONG because the answer is 2.4x106

    What do you think???
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 10, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Your answer looks correct to me.
     
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