Work/Potential Energy of a Spring

  1. 1. The problem statement, all variables and given/known data

    a)how much work is done by gravity as a 2kg mass is raised 2m vertically?

    b)what is the change in gravitation potential energy of a 2kg mass raised 2m vertically?

    c)How much work is done by a spring with a spring constant k = 50N/m as it is compressed by 0.1m from its relaxed position?

    d) what is the change in the potential energy of a spring with spring constant k = 50N/m as it is compressed by0.1m from is relaxed position?

    e) A 0.05kg mass is held against a spring( with spring constant k = 50N/m) while the spring is compressed by 0.1m. The mass is released and accelerated by the spring. What is the final speed of the mass?

    3. The attempt at a solution

    A. Wg= mgh wg = (2)(9.8)(2) = 39.2J
    B. PE = mgh PE = (2)(9.8)(2) = 39.2J
    C. Ws = 1/2kx^2 Ws = 1/2(50)(.1)^2 = 0.25J
    D. Us = 1/2 kx^2 Us = 1/2(50)(.1)^2 = 0.25J
    E. I dont know....
    W = change KE
    attempt 1/2kx^2 = 1/2mv^2
    1/2(50)(.1)^2 = 1/2(.005)v^2
    vf = sqrt(10)m/s


    can someone check my work?
    I need some help and explanation for problem e.
    Im not too sure about the signs.
     
  2. jcsd
  3. gabbagabbahey

    gabbagabbahey 5,009
    Homework Helper
    Gold Member

    You seem to be missing a few negative signs...It might help you to find them by looking at the definition of work done by any force [itex]\textbf{F}[/itex] in moving an object form point [itex]\textbf{a}[/itex] to point [itex]\textbf{b}[/itex]...what is that definition (it involves an integral and a dot product)?
     
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