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Find the maximum distance the spring is compressed.

  1. Mar 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A block of mass 2.0kg is dropped from height h=70cm onto a spring of spring constant k=1960 N/m. Find the maximum distance the spring is compressed.

    2. Relevant equations
    KE initial + PE initial = KE final + PE final
    KE = 1/2(mass)(velocity)^2
    PE = mgh or, when dealing with a spring, PE = 1/2 (k)(compression distance)^2

    3. The attempt at a solution

    The initial velocity is zero, so the initial KE is zero
    The final height is zero so the final PE is zero

    2kg(9.8)(.7m) = (1/2)(1960)x^2

    where x is the distance the spring is compressed
    solve for x.... x = .118m
    but it is not the right answer....

    Any help is appreciated,
  2. jcsd
  3. Mar 17, 2008 #2
    Hint: before the block falls on the spring, the gravitational potential energy is not mgh since the spring compresses a bit.
  4. Mar 17, 2008 #3
    but I thought if I wanted to calculate the total amount the spring compressed, the amount of energy at the very end of the fall (the instant before hits the spring-before it compresses) should equal the amount of energy the block has when it stops on the spring.... I am very confused!
    Should KE at the end of the fall = (1/2)(1960)x^2 ?
  5. Mar 17, 2008 #4
    That would be true if the spring somehow compressed without the top end of the spring actually being compressed downward, which is impossible.
  6. Mar 17, 2008 #5
    I'm sorry~ I'm still not quite sure I understand:
    so as the block hits the spring:
    1/2m(vinitial)^2 + 1/2k(xinital)^2 + mgh = 1/2k(xfinal)^2
    if x final = 0, then the whole thing = 0... which doesn't work out very well (square root of a negative number...)
  7. Mar 17, 2008 #6
    Set your 0 point so that at the point where the spring is compressed at its lowest point, that is your h = 0. So then how far above the lowest point is the block before you let it go?
  8. Mar 17, 2008 #7
    x + .7 meters?
  9. Mar 17, 2008 #8
    Now you can move on.
  10. Mar 17, 2008 #9
    Thank you!!
    (they should make a monument to super physics people like you)
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