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Speed of a Roller Coaster, Conservation of Energy

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data

    A roller coaster travels on a frictionless track as shown in the figure.
    (a) If the speed of the roller coaster at Point A is 5.0 m/s, what is its speed at Point B?
    (b) Will it reach Point C?
    (c) What speed at Point A is required for the roller coaster to reach Point C?

    Please view the attached figure. In case the image is too blury, the height of Point A = 5.0 meters, and the height of Point C = 8.0 meters.

    2. Relevant equations

    KE = 0.5*m*v^2
    PE = m*g*y, where y = vertical position

    3. The attempt at a solution

    KE = PE
    0.5*m*v^2 = m*g*y
    mass cancels
    0.5*v^2 = g*y
    v = √(2*g*y)

    What confuses me is what to do with the starting speed at Point A, 5.0 m/s. If the velocity at the top was zero, then the problem would be relatively straightforward. Where do I go from here? Thanks in advance!
     

    Attached Files:

  2. jcsd
  3. Nov 6, 2011 #2
    A) PE at point a and KE = KE at point b
    So m*g*h + 0.5*m*u^2 = 0.5*m*v^2
    I think you can do the rest
    B) Nope
    C) KE lost = PE gained
    I cant see the numbers on the image attached!
     
  4. Nov 6, 2011 #3
    Excellent, thank you!
     
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