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Conservative Forces and work done

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data

    A single constant force F = (3i + 5j) N acts on a 4.00 kg particle. Calculate the work done by this force if the particle moves from the origin to the point having the vector position r = (2i - 3j)m.

    2. Relevant equations
    W= Fr
    Wg= mgy1-mgy2
    Wc= Ui - Uf

    3. The attempt at a solution
    First I converted the friction and position coordinates to a single number.
    Then I tried to simply multiply the force and position but it was incorrect.
    The equations my book gave me was for gravity, spring, and potential but I feel like these equations don't fit in with the problem. What am I doing wrong?

    Thank you for your time!
  2. jcsd
  3. Feb 22, 2010 #2
    The force you've provided is a conservative force since [itex] \rm \overrightarrow{\bigtriangledown} x \overrightarrow{F} =0[/itex], so you can find the potential energy function using

    [itex] U = - \int \overrightarrow{F}_c \cdot d\overrightarrow{r} = -\int (F_x dx + F_y dy +F_z dz) +C[/itex] and
    then find the work, [itex] W_c = -\Delta U[/itex] .
    Last edited: Feb 22, 2010
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