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Conservation of energy up a ramp.

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose there is a block attached to a spring with spring constant [itex]k[/itex]. The block is pushed so that it compresses the spring a distance [itex]x_1[/itex]. The block is released and slides without friction up a ramp, coming to a maximum height [itex]h_1[/itex] above the ground. Suppose we compressed the spring twice as far, what maximum height does the block now reach?


    2. Relevant equations
    [itex]SPE = \frac{k x^2}{2}[/itex]
    [itex]GPE = m g h[/itex]


    3. The attempt at a solution
    Conservation of energy, for the first situation then the second:
    [itex]SPE=GPE[/itex]
    [itex]\frac{k x_1^2}{2} = mgh_1[/itex]
    [itex] h_1=\frac{k x_1^2}{2mg}[/itex]

    [itex]SPE=GPE[/itex]
    [itex]\frac{k (2 x_1)^2}{2} = mgh_2[/itex]
    [itex] h_2=\frac{k 4x_1^2}{2mg}[/itex]

    [itex]\frac{h_2}{h_1} =\frac{k 4 x_1^2}{2mg} * \frac{2mg}{k x_1^2} = 4[/itex]

    However the answerI have (this is from a course I took a long time ago) says it goes [itex]\sqrt{2}[/itex] times as high. Did I do something stupid here?
     
  2. jcsd
  3. Feb 25, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I agree with your result.
    Maybe the original question was the other way round? If the height should double, which factor do you need for the spring?
     
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