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Determine work on a spring.

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    If it requires 5.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additioanl 4.0 cm?

    2. Relevant equations

    Force done on spring: ##F_P = kx ##
    Work: ##\frac {1}{2}kx^2 ##

    3. The attempt at a solution

    I solved for K and got 25000.
    Plugging it into the equation for the work on a spring, I get ##\frac {1}{2}(25000)(0.06)^2 ## where 0.06 is the total length stretched. Doing it that way, I get the right answer.

    However, why can't I use the original information (5 J) and simply add it to the remaining 4 cm? ##5 + \frac {1}{2}(25000)(0.04)^2 ## Work is area under the force/displacement graph. Therefore, both ways should work, but that's the case.
     
  2. jcsd
  3. Mar 25, 2015 #2

    SammyS

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    That's because ##(0.06)^2\ne(0.02)^2+(0.04)^2\ ## .
     
  4. Mar 25, 2015 #3

    haruspex

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    Your force-displacement graph should be a triangle. Mark O, A, B, C at 0, 2, 4, 6 cm on the x axis, with D, E, F on the slope above A, B, C respectively. You want area ACFD. You won't get that by adding OAD to OBE.
     
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