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Homework Help: Springs & circular motion

  1. Nov 7, 2009 #1
    1. The problem statement, all variables and given/known data

    A small block is launched on the fricntionless loop the loop shown. te sprink launcher has a sprink constant k

    a)find the velocity at the top of the loop as a function of the displacement x of the spring launcher from its equilibrium length

    b)find the minimum cvalude of x such that the block goes over the top in contact with the track

    c)find the normal force on the bock A as a function of x

    2. Relevant equations

    3. The attempt at a solution

    I believe i would have to use .5ks2, and then calculate the acceleration, and aply it to uniform circular motion, is this correct

    W = .5kx2

    K = .5mv2

    v = (2W/m).5 = (kx2/m).5
    Last edited: Nov 7, 2009
  2. jcsd
  3. Nov 8, 2009 #2
    ok pretend my first attemp never happened

    Part A
    TA = .5ks2
    UA = 0

    TB = .5mv2
    UB = -2Rmg

    .5ks2 = .5mv2 - 2Rmg

    v = ((ks2 + 4Rmg)/m).5

    Part B

    same as above, just solved for s

    s = ((mv2-4Rmg)/k).5

    Part C

    not really sure about the Normal Force, Does it still point up even if its on the top of the loop the loop
  4. Nov 8, 2009 #3


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    Homework Helper

    When the block is moving in the loop, two forces are acting. One centripetal force and the other the weight of the block. Mg*cosθ contributes to the normal reaction.
  5. Nov 9, 2009 #4
    so the normal is

    N = mgcos(180)

    do u agree with my other responses, they do not match what the answer is said to be

    Part B answer is xmin = (5mgR/k)1/2

    Part C answer is N(x) = (kx2/R) - 5mg

    where does that 5 mg come from
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