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Find the maximum deflection of the spring

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data
    The 3.8-kg collar is released from rest at A and slides down the inclined fixed rod in the vertical plane. The coefficient of kinetic friction is 0.51. Calculate (a) the velocity v of the collar as it strikes the spring and (b) the maximum deflection x of the spring.

    I have attached an image of the question.

    2. Relevant equations

    3. The attempt at a solution

    I was able to find the velocity of the collar with:

    U1 + K1 = U2 + K2 + F

    K1 and U2 are 0

    F is the friction force

    0.5mv2 = mgh1 - F

    Drawing a FBD of the collar shows that the Normal force (F = ukN):

    N = mgsin(27)

    0.5(3.8kg)v2 = (3.8kg)(9.81 m/s2)(0.57sin(63)) - (0.51)(0.57m)(3.8kg)(9.81m/s2)sin(27)

    Solving for v gives me:

    v = 2.7157

    I can't seem to find the displacement of the spring though.

    I realize that F = -kx and I need to find F to get x.

    Looking at the practice question (identical scenario but different numbers) led me to believe that the answer should be:

    F = mg - mgsin(27)

    x = sqrt[mg-ukmgsin(27)/2700]

    x = 103 mm
    But it says this isn't correct and I'm not sure where I'm making my mistake.

    Help is appreciated.

    Attached Files:

  2. jcsd
  3. Feb 23, 2013 #2


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    Note that force and energy have different dimensions, so they can't be added together.
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