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Conservation Of Energy, Block Sliding Down Incline Onto Spring.

  1. Oct 8, 2013 #1
    1. The problem statement, all variables and given/known data
    CNf8k2D.png
    A block of mass m starts from rest at a height h and slides down a frictionless plane inclined at angle θ with the horizontal, as shown below. The block strikes a spring of force constant k.
    Find the distance the spring is compressed when the block momentarily stops. (Let the distance the block slides before striking the spring be l. Use the following as necessary: m, θ, k, l, and g.)

    2. Relevant equations
    Conservation of Energy:
    GPE : U = mgh
    K = (1/2)mv2
    Spring = (1/2)kx2


    3. The attempt at a solution

    My Diagram: QJ9jkix.jpg
    Let H = l*sinθ
    Let h = x*sinθ

    Moment 1: E = mg(H+h) = mgsinθ(l+ x)

    Moment 2: E = (1/2)mv2 + mgh = (1/2)mv2 + mgx*sinθ

    Moment 3: E = (1/2)kx2

    -------- Attempts to get rid of x2 led to
    x = h/sin
    (1/2)k(h/sinθ)2 = mgsinθ(l+ x) ;;;
    (kh2/2sin2θ) = mgsinθ(l+ x) ;;;
    (kh2/2) = mglsin3θ + mgxsin3θ ;;;
    (kh2/2) - mglsin3θ = mgxsin3θ ;;;

    x = k*h2/2mgsin3θ - l
     
  2. jcsd
  3. Oct 8, 2013 #2

    Doc Al

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    Staff: Mentor

    This is good.

    Don't try to express things in terms of "h"--that's an unknown directly related to "x".

    Hint: Just compare moments 1 and 3. Solve that equation!
     
  4. Oct 8, 2013 #3

    ehild

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    Homework Helper
    Gold Member

    As h=xsinθ, your last equation does not give x explicitly in terms of the known quantities, k, m, θ, L, and g.

    ehild
     
  5. Oct 8, 2013 #4
    So by solving equations 1 and 3 I got
    mglsinθ+mgxsinθ = (1/2)kx2
    0 = (k/2)x2 - mgsinθx - mglsinθ
    quadratic formula

    x = (mgsinθ ± √[mgsinθ(mgsinθ+2kl)] ) / k
     
  6. Oct 8, 2013 #5

    ehild

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    Homework Helper
    Gold Member

    It is all right now.

    ehild
     
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