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 5,015
    Homework Helper
    Gold Member

    Chegg
    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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