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A mass-spring system with recoil and friction

  1. Mar 20, 2007 #1
    An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction, mu , between the object and the surface. The object has speed v when it reaches x=0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When the object reaches x=0 on its return trip, it stops.


    Find k, the spring constant.
    Express k in terms of mu, m, v, and g .

    Any ideas how on setting this up? KE1 + SPE1 = KE2 + SPE2 is where I'm headed...
     
  2. jcsd
  3. Mar 20, 2007 #2

    Hootenanny

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    Your on the right track with conservation of energy, however, don't forget the energy dissapated due to friction.
     
  4. Mar 20, 2007 #3
    This is what I've done so far

    Work-energy theorem: E_f-E_i=W_fr:

    0-(1/2)*m*v^2=- mu*m*g*2*x

    x = .5v^2 / (2g(mu)) Max compression of spring

    W=-mu*m*g*x

    E_i=(1/2)*m*v^2 )

    E_f=(1/2)*k*x^2

    Work-energy theorem:

    (1/2)*k*x^2-(1/2)*m*v^2=-mu*m*g*x

    Plugged into x and solved for k and got 2m(mu)g...answer was incorrect. Any ideas?
     
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