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Calculate minimum value of force for a cart

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Given the diagram shown, calculate the minimum value of h such that when the cart reaches point A, it is just about to fall off.

    R = 10m
    mass of cart = 158kg
    note: there is no friction in the entire system

    2. Relevant equations
    ΣFc = mac
    (note: Fc = centripetal force and ac = centripetal acceleration)


    3. The attempt at a solution
    I am not sure if I got this question right but here is what I did:

    First I drew a free body diagram for the part of the diagram that had centripetal forces acting on it (included in the attachments).

    Then for my calculations I started out with the equation ΣFc = mac first and here is what I did:

    ΣFc = mac
    Fn + Fg = mv^2/r (Fn cancels out therefore):
    Fg = mv^2/r
    mg = mv^2/r (the m's cancel out)
    g = v^2/r
    (g)(r) = v^2
    (9.80)(10) = v^2
    98 = v^2

    there is no friction in the system therefore:
    ΔE = 0
    (Epf - Epi) + (Ekf - Eki) = 0
    Epf - Epi + Ekf - Eki = 0
    Epf + Ekf = Epi + Eki (Eki = 0 therefore):
    Epf + Ekf = Epi
    mghf + 1/2mvf^2 = mghi (the m's cancel out):
    ghf + 1/2vf^2 = ghi
    (9.80)(2*10) + 1/2(98) = (9.80)hi (for here I put hf = 2R because the cart is at the very top of the loop here so therefore hf = 2 times the radius)
    245/9.80 = hi
    25m = hi

    My question is, could someone please check this question to see if I did it right or if my answer is right, because I have three questions following this one that are quite similar in setup so I just want to make sure I am doing the first one correctly before I move onto the other three.
     

    Attached Files:

    Last edited: Dec 3, 2008
  2. jcsd
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