# Conservative Forces and work done

1. Feb 22, 2010

### cinderblock

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?

The force you've provided is a conservative force since $\rm \overrightarrow{\bigtriangledown} x \overrightarrow{F} =0$, so you can find the potential energy function using
$U = - \int \overrightarrow{F}_c \cdot d\overrightarrow{r} = -\int (F_x dx + F_y dy +F_z dz) +C$ and
then find the work, $W_c = -\Delta U$ .