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Calculate total mechanical energy of a frictionless spring

  1. Feb 22, 2016 #1
    Hi,
    Could you please help me determine if I've worked this problem out correctly.

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


    A 2.86-kg object on a frictionless horizontal surface oscillates at the end of a spring with an amplitude of
    7.81 cm. Its maximum acceleration is 3.74 m/s2.
    Calculate the total mechanical energy.

    2. Relevant equations

    1) Total Mechanical Energy: E = 0.5 k A^2
    2) Spring Constant: k = m w^2 (where w = angular velocity)
    3) Acceleration : a = -w^2 x

    3. The attempt at a solution

    Given the Amplitude A, we must calculate the spring constant k to calc the total mechanical energy.

    First find w using formula 3)
    w = - sqr( a / x)
    w = - sqr(3.74 / 0.0781)
    w = - 6.92

    Now substitute k in formula 1 with formula 2 to calculate the total mechanical energy.

    E = 0.5 (m w^2) A^2
    E= 0.5 (2.86) (-6.92)^2 (0.0781)^2
    E= 0.0418 Joules
     
  2. jcsd
  3. Feb 22, 2016 #2

    gneill

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    Staff: Mentor

    Your method is fine.

    Re-do your final calculation; you seem to have slipped a decimal point.
     
  4. Feb 22, 2016 #3
    Yes it's okay but pay attention at this:

    a= -ω^2 x ---> ω= √(-a/x)

    Since a is opposite to x a= -3.74 m/s^2 and ω= 6.92 rad/s so ω>0
     
  5. Feb 22, 2016 #4
    Thank you for the feedback and for checking my shoddy calculation.

    I redid the calculation and the answer came to 0.418 Joules
     
  6. Feb 22, 2016 #5

    haruspex

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    Science Advisor
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    2016 Award

    You mean, so ω is real. Whether you choose to take the positive or negative root is another matter.
     
  7. Feb 22, 2016 #6
    Yes, I just focused on the fact that he got a ω< 0 by making a little mistake in solving a= -ω^2 x

    :)
     
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