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Conservation of mechanical energy vs sum of forces

  1. Oct 26, 2014 #1
    When do one use the principle of conservation of mechanical energy to find the velocity of a mass, and when would you use the sum of forces equals to the mass times acceleration, and there after use a ds=v dv in order to find the velocity.

    The specific question related to this is a spring fixed to a mass which is pulled up a slope by a constant force. They want the final velocity. I already have the force in terms of distance that the spring applies of the mass. I have the constant force etc.

    I used sum of F's = ma and a ds = v dv in order to find velocity. In the memo however They used conservation of energy: T1 +V1 +U1-2 = T2 +V2. My answer is different to the memo. Should'nt the answer be the same? and if not? Whats the two cases that splits these two methods of approach?
     
    Last edited by a moderator: Oct 26, 2014
  2. jcsd
  3. Oct 26, 2014 #2

    berkeman

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    Staff: Mentor

    Yes, the answers should be the same. Can you post the detailed work for both methods? We can help to find the error(s). :-)
     
  4. Oct 26, 2014 #3
    Question: calculate speed of block at final position.
    GIven: block on slope of 15 degree incline attached to spring; spring applies force down the slope with stiffness of 450 N/m; frictional coefficient= 0.28 kinetic and 0.3 static; constant force of 150N applied up the slope; final position has spring stretched to 0.2m; initial position has string unstretched and block velocity of 0 m/s.

    Calculated: work done by applied force=30J ; work done by frictional force= -4,327; potential energy of spring in final position = 9J.

    According to work energy theorem (memo):
    T1+V1+U1-2=T2+V2
    0+0+30-4,327=0.5 * (80/9) * (V squared)+9+4,141
    V=1,753 m/s


    According to sum of forces:
    sum of F = ma
    150-80sin15 - 21,64-450x=80a
    a=1,346 - 5,625x

    since a ds=v dv

    integrate...
    1,346*0,2-(5,625/2)*(0.2 squared)=0,5*(V squared)
    V=0,56 m/s

    Thanks for the help
     
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