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Conservation of Energy and Springs

  1. Nov 6, 2014 #1
    1. The problem statement, all variables and given/known data
    A mass starts from rest and slides a distance d down a frictionless θ deg incline. While sliding, it comes into contact with an unstressed spring of negligible mass, as shown in the figure below. The mass slides an additional distance as it is brought momentarily to rest by compression of the spring . Calculate the initial separation d between the mass and the spring. (I am given mass, the angle, additional distance, and spring constant)

    2. Relevant equations
    Energy is conservative

    3. The attempt at a solution
    I got the answer in my textbook after two attempts
    However my first attempt I've been wondering.
    The final energy equation that I originally came up with did not work
    But I'm thinking about it like this: if the spring is at an angle, wouldn't there also be a gravitational potential energy at the end as well? It's on a ramp, and the spring keeps it on the ramp. It doesn't ever tell us to consider that the mass actually slides onto ground level.
    I had Initial Gravitational Potential Energy = Final Potential Energy Of the Spring + Final Gravitational Potential Energy (well I couldn't really solve it since I couldn't figure out how far above it was afterwards since there wasn't a distance of the whole ramp)
    The method that worked was that Initial gravitational potential energy = final potential energy of the spring
    I have a picture of how I visualized it, the red line just represents how high up it is from the ground.
    (Left side is initial, right side is final. Just ignore the size difference)
    Please note, (restating) that I did get the answer in the end. I'm just asking a question of why it isn't another solution
     

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    Last edited: Nov 6, 2014
  2. jcsd
  3. Nov 6, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Sure.
    You can combine both parts to a single distance, that makes equations easier.
     
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