# Compute the work done by the force field.

1. Dec 16, 2012

### bfusco

1. The problem statement, all variables and given/known data
compute the work done by the force field F(xyz)=[(yze^(xyz)+y^2+1)i+(xze^(xyz)+2xy)j+(xye^(xyz))k], in moving the object along the path C from beginning to end. here C is the path paramterized by r(t)=<t, (t^2)-1, t+2>, 0<_t<_1.

3. The attempt at a solution
Would i be correct if i said that i should use the functions of x(t), y(t), z(t), and substituting them into the original equation? then take the derivative of r(t) and do the dot product of them. then use the formula: ∫F*dr?

2. Dec 16, 2012

### LCKurtz

If you mean$$\int_0^1\vec F\cdot \frac{d\vec R}{dt}\, dt$$then yes.

3. Dec 16, 2012

### haruspex

Some of that sounds right, other parts bewildering. To make it clearer, try it and post your working.

4. Dec 17, 2012

### HallsofIvy

Staff Emeritus
Actually, given that $\vec{r}(t)$ is a function of t, "$d\vec{r}$" is a reasonable way of writing "$(d\vec{r}/dt) dt$". But I would object to using the capital R when only "r" was given before.

5. Dec 17, 2012

### LCKurtz

Yeah, I used the capital letter out of habit. But my point was to make sure the OP understood the independent variable was $t$ and the use of the $t$ limits.