Relationship between work and potential energy

  1. 1. The problem statement, all variables and given/known data
    At time ti, the kinetic energy of a particle is
    35.5 J and its potential energy is 8.16 J.At
    some later time tf , its kinetic energy is 9.38 J.
    If only conservative forces act on the parti-
    cle, what is its potential energy tf ? Answer
    in units of J.
    If the potential energy at time tf is 6.95 J,
    what is the work done by the nonconservative
    forces acting on the particle? Answer in units
    of J.


    2. Relevant equations
    W=F*displacement*cos(theta)


    3. The attempt at a solution
    For the first part of the question, because there were only conservative forces, the sum of kinetic and potential must be same for both ti and tf. And i know that i have the right answer for that. But for the second part, where force isn't conserved, that would not be the case:
    I CANNOT take the sum of 35.5 and 8.16 and subtract 6.95 like i did for the first part.
    I dont think i completely understand the concept here, so i'd appreciate any help.
     
    Last edited: Jan 21, 2007
  2. jcsd
  3. You're missing a relationship between work and energy. W = ______

    Fill in the blank and you should have your answer. Hint (you're not looking for W = Fd)
     
  4. work is kinetic energy here, right?
     
  5. and what else...
     
  6. PhanthomJay

    PhanthomJay 6,252
    Science Advisor
    Homework Helper
    Gold Member

    No. When non-conservative forces act, total mechanical energy is not conserved. How much energy did you start with? What did you end up with? Can you explain this?
     
  7. well, I started with 43.66J. But i dont know how much ends up being left.
     
  8. wait... can this possibly be right?:
    W=KE+PE
     
  9. That's my line of thought...work done by non conservative forces= change in kinetic energy + change in potential energy
     
  10. so does the answer to this part end up the same as first part of the question?
     
  11. PhanthomJay

    PhanthomJay 6,252
    Science Advisor
    Homework Helper
    Gold Member

    No. The initial mechanical energy,
    (KE + PE)_initial, is 43.66J. The final mechanical energy, (KE + PE)_final, is 16.33J. The difference between the two represents the change in the total mechanical energy of the system , which is, as stated above, equal to the work done by the non-conservative forces.
     
  12. would the change in mechanical energy be negative?
    -27.33J in this case.
    because +27.33J is wrong, according to my hw service
     
    Last edited: Jan 21, 2007
  13. Assuming you did the calculation right, the work should be negative.
     
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