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Homework Help: A block dropped on a spring, distance compressed unknown.

  1. Mar 12, 2010 #1
    1.
    A block of mass m = 1.6 kg is dropped from height h = 61 cm (height above the spring, not total height) onto a spring of spring constant k = 1820 N/m (Fig. 8-38). Find the maximum distance the spring is compressed.


    2. Relevant equations

    K=-U, since all energy is conserved, work would equal zero.

    3. The attempt at a solution

    basically kinetic energy is zero, since its starts from zero and ends with zero.

    so i this means that the potential energy must equate.

    mgh (potential energy from block at H) = (kx^2)/2(potential energy from spring)

    so basically the height from the spring is disclosed, but the spring compression isnt.

    I tried this first

    mg(x+h)=1/2kx^2

    1.6kg * 9.8 m/s^2(x+.61cm)=910n/m *x^2


    but it gives me an awkward quadratic equation, where the number under the square root would be negative.

    I also tried to find to find the kinetic energy right before it touches the spring, and then apply it to the conservation of energy, where 1/2mvf^2=1/2kx^2 but that ddidnt work either, any suggestions?
     
  2. jcsd
  3. Mar 12, 2010 #2

    hotvette

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    Homework Helper

    Pls elaborate. What didn't work? Be careful with units (i.e. cm vs m).
     
  4. Mar 12, 2010 #3
    well basically i found the kinetic energy right as it hits the spring, by using the equation
    K=U.

    which would be 1/2mvf^2-1/2mvi^2=-mgh

    the initial velocity would be zero, so that cancels, and leaves me with

    1/2mvf^2=-mgh

    so i use the kinetic energy produced by the distance from the spring and plug it into the
    conservation of elastic energy equation

    -1/2mvi^2(kinetic energy produce by the drop)=1/2kx^2(potential elastic energy)

    but this equation didnt produce the correct answer either, and i actually dont know the answer since its an online hw assessment.
     
  5. Mar 12, 2010 #4

    hotvette

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    Homework Helper

    Looks good so far. What is your expression for x and why do you think the answer you got is wrong? What answer did you get by the way?
     
    Last edited: Mar 12, 2010
  6. Mar 12, 2010 #5
    Why would it give you a negative number? Did you put the equation to the form of ax^2+bx+c=0 before you start? -4ac is a positive number because a is negative and c is positive.
     
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