Is more work required for this spring?

  1. A spring with a force constant of 50 N/m is stretched continuously from x0=0 to x2=20 cm. Is more work required to stretch the spring from x1=10 cm to x2=20 cm than from x0 to x1? Justify your answer mathematically.

    I thought the work required is the same because the displacements are equal for both work equations... but I think I'm wrong.
     
  2. jcsd
  3. work = 1/2 kx^2

    so then the difference would be greater between 20cm and 10cm

    w= EPEf-EPEi = 0.5(k)400-0.5(k)100 = 150k
    w0->1 = 0.5(k)(100) - 0.5k(0) = 50k
     
  4. but wouldn't it be:
    work1 = 1/2 k (10cm)^2
    work2 = 1/2 k (20cm - 10cm)^2=work1
    ?
     
  5. no, the work is the difference between energies.

    [tex] EPE_i + W = EPE_f [/tex]
    [tex] W = EPE_f - EPE_i [/tex]
    [tex] W = 0.5kx_f^2 - 0.5kx_i^2 [/tex]
     
  6. I remember now...

    what does EPE mean?
     
  7. elastic potential energy
     
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