1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]\frac{k x_1^2}{2} = mgh_1[/itex]
    [itex] h_1=\frac{k x_1^2}{2mg}[/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


    User Avatar
    2017 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted