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Calculating work done by a spring when stretched

  1. Oct 15, 2010 #1
    1. The problem statement, all variables and given/known data

    At a certain point, when a spring is stretched near its elastic limit, the spring force satisfies the equation

    F = −α x + β x3 , where α = 12 N/m and β = 890 N/m3 .

    Calculate the work done by the spring when it is stretched from its equilibrium position to 0.15 m past its equilibrium.
    Answer in units of mJ.

    2. Relevant equations

    3. The attempt at a solution

    since this is a nonlinear curve i thought that the area under the curve would equal the work done by the spring at the .15 m

    so i integrated and got

    -6x2 + 222.5x4

    since the spring is starting at the equilibrium position, initial position is 0 and final position is .15m so

    -6(.15)2+222.5(.15)4 = -.02235

    this doesn't make sense since we are pulling the spring and the work should be positive right?
  2. jcsd
  3. Oct 15, 2010 #2


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    Yeah, but the problem asks for the work done by the spring, not the work done by the person pulling it.
  4. Oct 15, 2010 #3
    ok so maybe its negative because the spring would be working to go back to its equilibrium position. My answer is wrong though, what am i doing wrong?

    am i right in my approach? i really cant think of another way of going about it...

    a hint would be very nice
    Last edited: Oct 15, 2010
  5. Oct 15, 2010 #4
    if work = 1/2kx^2 then all i need to find is the constant k given the information... i dont see how i can do this because i dont know x for the given equation, it just tells me that its near its elastic limit
  6. Oct 15, 2010 #5


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    Work (actually, potential energy) does not equal 1/2 kx^2 in this case. That equation applies only when F = -kx per Hookes law. This spring does not follow that law. Your original solution looks correct to me, except you answered in joules , but the problem asked for the answer in milli-joules (mJ).
    -0.02235 J = ____?____ mJ ? (round it off to the nearest whole number).
  7. Oct 15, 2010 #6
    -22.35. Thanks a lot, I can't believe I didn't see that.
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