1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted