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Conservation of Energy

  1. Nov 4, 2007 #1
    1. The problem statement, all variables and given/known data
    A block of mass m = 2.0 kg is dropped from height h = 55 cm onto a spring of spring constant k = 1960 N/m. Find the maximum distance the spring is compressed.


    2. Relevant equations
    [tex]\Delta K+ \Delta U_G+ \Delta U_S=0[/tex] \change in kinetic energy+change in gravitational energy+change in spring energy=0
    [tex]\Delta K=0[/tex]
    [tex]U_{Gf}-U_{Gi}+U_{Sf}-U_{Si}=0[/tex]
    [tex]U_{Si}=0[/tex] can be assumed
    so
    [tex]U_{Sf}=U_{Gi}-U_{Gf}[/tex]


    3. The attempt at a solution
    resumed from above:
    [tex]\frac {kx_f^2}{2}=mgy_i-mgy_f[/tex]
    so: [tex]\frac {kx_f^2}{2}=mgy_i-mgx_f[/tex]
    With this I have tried over and over to solve for [tex]x_f[/tex] but I cannot find any way of getting [tex]x_f[/tex] by itself.
    edit:LaTeX formatting
     
  2. jcsd
  3. Nov 4, 2007 #2
    conservation of energy, [tex]\Delta[/tex]U(g)+ [tex]\Delta[/tex]U(spring) = 0 <=== look, all the energy lost from one object goes to the other, so the sum is 0. Remember! conservation of energy. Think about it.

    [tex]\Delta[/tex]U(g)=-[tex]\Delta[/tex]U(spring) <===== moved that equation around a it... just algebra.

    mgh2-mgh1 = (1/2)kx^2 <===== look what we have here if we make it look more detailed with what we know.

    Or simply mgh=-(1/2)kx^2
     
    Last edited: Nov 4, 2007
  4. Nov 4, 2007 #3

    hage567

    User Avatar
    Homework Helper

    It's a quadratic equation.
     
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