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Spring Speed Problem

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data
    A spring whose stiffness is 3500 N/m is used to launch a 4 kg block straight up in the classroom. The spring is initially
    compressed 0.2 m, and the block is initially at rest when it is released. When the block is 1.3 m above its starting
    position, what is its speed?


    2. Relevant equations
    System: block, spring and earth.
    delta_Uspring + delta_Ugravitation + delta_K=0


    3. The attempt at a solution
    everything i've tried seems to be wrong, the answer answer given to us however is 3.09 m/s.
     
  2. jcsd
  3. Nov 9, 2009 #2

    PhanthomJay

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    timmy8, welcome to PF!

    Your equation is correct, so please show your work so we may see where you may have gone wrong.
     
  4. Nov 9, 2009 #3
    1/2(3500)(1.3^2)-1/2(3500)(0.2^2)+4(-9.8)(1.3-0.2)+1/2(4)Vf^2-1/2(4)(0^2)=0

    from there i solved for vf^2;

    and vf^2=-1422.19

    i am getting Vf^2 to be a negative number and i would have to solve the square root of that to get Vf.
    what am i doing wrong?
     
  5. Nov 9, 2009 #4

    PhanthomJay

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    You have the change in the spring potential energy wrong. What is the PE of the spring when the block rises 1.3 m above its start point? The block is not attached to the spring. Also, you seem to have slipped up on a plus /minus sign for the change in gravitational PE. Also, the problem asks for the speed at 1.3 m above the initial start position of the block (when the spring is initially compressed, I think).
     
  6. Nov 9, 2009 #5
    so in the spring potential should Uf be equal to zero? and for the change in gravitational PE isn't the formula m*g*delta_h? I am so lost.
     
  7. Nov 9, 2009 #6

    PhanthomJay

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    yes
    Yes, the formula is change in Gravitational PE is (mgh_final) - (mgh_initial). final h is 1.3 and initial h is zero, so the change is positive (it has gained grav. PE).
     
  8. Nov 9, 2009 #7
    i thought g would be -9.81?
     
  9. Nov 9, 2009 #8
    now i have:
    -springPE +mgh_final+1/2(m)v_final^2=0

    This gave me the correct answer.

    thank you for all your help PhantomJay
     
  10. Nov 10, 2009 #9

    PhanthomJay

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    You're welcome. The plus and minus sign can be a killer in Physics, and it is easy to get confused. Sometimes you just have to reason it out.
     
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