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Calculating the decrease in kinetic energy of an object as it moves against a spring

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A 5-kg object initially slides with speed V0 in a hollow frictionless pipe. The end of the pipe contains two springs, one nested inside the other, as shown above. The object makes contact with the inner spring at point A, moves 0.1 meter to make contact with the outer spring at point B, and then moves an additional 0.05 meter before coming to rest at point C. The graph shows the magnitude of the force exerted on the object by the springs as a function of the object's distance from point A.
    a. Calculate the spring constant for the inner spring.​
    b. Calculate the decrease in kinetic energy of the object as it moves from point A to point B.​
    c. Calculate the additional decrease in kinetic energy of the object as it moves from point B to point C.​
    d. Calculate the initial speed V0 of the object.​
    e. Calculate the spring constant of the outer spring.​

    m = 5 kg
    ΔxA-B = 0.10 m
    ΔxB-C = 0.05 m
    Vat C = 0 m/s

    (Here are the diagram and the graph. Sorry if they're less than beautiful, I just quickly recreated them on MS Paint)

    34gncsz.png

    2up94z9.png

    2. Relevant equations

    F=kx
    Uelastic=(1/2)kx2
    Kinematic Equations

    3. The attempt at a solution

    According to the graph, F=20 N when the object is at B, and it's displacement at B (relative to the point at which it first made contact with the inner spring) is 0.10 m. So:
    F = kx
    20N = k(0.10m)
    k = 200 N/m

    As for part b, I don't really know where to start. Would I calculate Uelastic to find the decrease in kinetic energy? I have no idea how to do c, d, or e, either...
     
  2. jcsd
  3. Sep 25, 2012 #2
    Re: Calculating the decrease in kinetic energy of an object as it moves against a spr

    Use energy conservation. The loss in kinetic energy corresponds to an increase in the potential energy due to the spring.
     
  4. Sep 25, 2012 #3
    Re: Calculating the decrease in kinetic energy of an object as it moves against a spr

    According to the graph, F=20 N when the object is at B, and it's displacement at B (relative to the point at which it first made contact with the inner spring) is 0.10 m. So:
    F = kx
    20N = k(0.10m)
    k = 200 N/m
    ----------
    F is not constant.
    You can find work done on the spring, Fx, as an area under the graph.
    The work done on the spring is stored as potential energy, 1/2 kx2
     
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