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Homework Help: Energy Lost to Heat ~ Spring

  1. Mar 14, 2012 #1
    Energy Lost to Heat ~ Spring (Solved)

    1. The problem statement, all variables and given/known data
    --->What is the energy lost to heat?<---

    spring mass = 15g = .015kg
    spring constant = 220 J/m^2
    spring is compressed 5cm (.05m) then released to achieve maximum height of 102 cm (1.02 m)

    2. Relevant equations
    U = .5(k)(x)^2 where U is the potential energy of a spring, k is the spring constant, and x the compression length.

    K=.5(m)(v)^2 where K is kinetic energy, m is a mass, and v is velocity

    Ug = mgy where Ug is gravitational potential energy, m is a mass, g is gravity, y is height in y direction

    ME (Mechanical Energy) = Kinetic Energy K + Potential Energy (Ug)

    3. The attempt at a solution
    Ok, I understand that this is a Conservation of Energy question. I don't know how to go about it.

    I need to find energy lost to heat.

    U = .5(220J/m^2)(.05m)^2
    = 0.275 Joules <--Spring potential energy

    At it's highest point...Kinetic Energy = 0 and Potential Energy is at its greatest.

    Ug= mgy
    = (.015kg)(9.81m/s^2)(1.02m)
    = .15J


    This is where I'm lost, would anybody mind pointing me in the correct direction?
    Last edited: Mar 14, 2012
  2. jcsd
  3. Mar 14, 2012 #2
    as mechanical energy is conserved. so no energy is lost as heat.
  4. Mar 14, 2012 #3
    Heat is counted as energy...
  5. Mar 14, 2012 #4


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    Staff Emeritus
    Science Advisor
    Gold Member

    In this problem, are you saying that the compressed spring, after being released, *jumps into the air* and reaches a height of 1.02 m?

    If so, then you basically have the answer. If mechanical energy had been conserved, then all of the initial elastic potential energy stored in the spring ought to have been converted into gravitational potential energy when the spring reached its max height.

    However, the gravitational potential energy at max height is clearly less than the initial elastic potential energy that was stored.

    So the difference must have been dissipated as heat.
  6. Mar 14, 2012 #5
    That easy!? Haha, thank you!
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