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The coefficient of friction by spring compression

  1. Feb 19, 2015 #1
    1. The problem statement, all variables and given/known data
    A box has the mas 50.0Kg. The box slides on a horizontal surface that has friction. The box has the velocity 3.00m/s when its 0.600m away from a spring with negligible mass and the force coefficent 20Kn/m. The box hits the spring and comes to a momentary rest after compressing the spring 0.120m before shooting off into the opposite direction.

    A ) [solved] What is the work that the spring exerts on the box as it slows down?
    Assuming I did this correctly: Then the spring exerts 144J of energy onto the box.

    B ) [Unsolved] What is the coefficent of kinetic friction that acts on the box?


    Relevent equations include (I assume) Hooks law and the equations of conservation of energy and motion.

    W = F * S
    F = MA
    Fk = MGμ
    E = -KΔx
    E = 0.5*m*v2


    What I've done:

    Now, I started by trying to evaluate at what speed the box hits the spring based on the compression. I started thinking that I could just use the conversation of energy to connect 0.5*m*v2 = -KΔx and solve for v. But then I thought that this wouldn't be accurate since a small amount of the energy must have gone into the friction over those 0.120m and thus the velocity would be incorrect. I was thinking that maybe I'd use the force that the spring exerted on the box from A) but I'm not quite sure how I should approach this problem correctly.

    So to sum up:

    Given the compression of a spring hit by a box of mass m how can I calculate the kinetic friction?
     
  2. jcsd
  3. Feb 19, 2015 #2

    Doc Al

    User Avatar

    Staff: Mentor

    First figure out how much work must have been done by friction.
     
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