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Did I do this question correctly?

  1. Mar 17, 2009 #1
    Consider the frictionless roller coaster shown:
    http://i299.photobucket.com/albums/mm286/lanvin12/physics-2.jpg [Broken]

    If a 12 000-kg car starts at rest from Point A, calculate

    a) the total energy of the system

    b) the speed of the car at point B

    c) the force that must be applied to bring it to a stop at point E

    d) the work done to bring it to a stop at point E


    Here's what I did...

    a)
    E(T) = E(K) + E(P)
    = 1/2(mv^2) + mgh
    =1/2(12000 x 0) + (12000 x 9.8 x 95)
    =1.1x10^7 J

    b)
    E(T1) = E(T2)
    1/2(V1^2) + gh(1) = 1/2(v2^2) + gh(2)
    9.8 x 95 = 1/2(v2^2) + (9.8 x 65)
    931 = 1/2(v2^2) + 637
    V(2) = 24m/s

    c)
    1/2(V1^2) + gh(1) = 1/2(v2^2) + gh(2)
    9.8 x 95 = 1/2(v2^2) + (9.8 x 25)
    V(2) = 37.04m/s

    F = mass ([Vf^2 - Vi^2] / [2 x delta d])
    = 12000 ([0^2 - 37.04^2] / [2 x 7])
    =-3.2x10^4 J

    d)
    W=E(K)
    =1.1x10^7 J

    Do you see any mistakes?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 17, 2009 #2

    LowlyPion

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    Welcome to PF.

    Mostly good.

    c) however must have a stopping force that absorbs all the potential energy, as in d) which you figured correctly.
     
  4. Mar 17, 2009 #3
    Thanks.

    I don't think I understand...? I just used the formula F = ma for c). Do I change my answer to a positive? And I'm not sure how to fix d)...
     
  5. Mar 17, 2009 #4

    LowlyPion

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    Not quite.

    That's incorrect. That gives the KE at the top of the last hill. It's the whole 95 m of PE that needs stopping
     
  6. Mar 17, 2009 #5
    c)
    I think I need to change my approach?
    F = W/d
    =(1.1x10^7 J) / 7m
    =1.6x10^6 J

    d)
    W=E(P)
    =1.1x10^7 J
    ...I thought the work required to stop the roller coaster is equal to the total energy of the system?
     
  7. Mar 17, 2009 #6

    LowlyPion

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    It is.

    But you could have done it the first way too by taking all the potential as kinetic energy and figuring deceleration.

    But not J for force.
     
  8. Mar 17, 2009 #7
    oops... my mistake!
    c)
    F = W/d
    =(1.1x10^7 J) / 7m
    =1.6x10^6 N
     
  9. Mar 17, 2009 #8
    Just to confirm, did I finally do c) and d) correctly?
     
  10. Mar 17, 2009 #9

    LowlyPion

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    Looks OK. Total energy from potential needs to be accounted for after all.
     
  11. Mar 17, 2009 #10
    Thank you!
     
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