Calculating Work Done Using Force Vector & Distance

[somebodyelse5]

Homework Statement

A constant force F=4i+2j+2k moves an object along a straight line from the point (1, -5, 1) to the point (1, -1, 0).

Find the work done if the force is measured in Newtons and the position is measured in meters.

Homework Equations

W=Fd

The Attempt at a Solution

I used the distance formula to find the distance between the two points which is sqrt(17)

But what is the correct way to multiply the Force vector by this distance?

 

[Phrak]

1. Add up the x y and z components of work or 2. use the dot product of F and D, where D is the displacement.

 

[gabbagabbahey]

Homework Equations

W=Fd

You should get in the habit of using the more general definition of work from $\textbf{r}_1$ to $\textbf{r}_2$:

$$W=\int_{\textbf{r}_1}^{\textbf{r}_2} \textbf{F}\cdot d\textbf{r}$$

In your case, $\textbf{F}$ is uniform so you can pull it out of the integral

$$W=\textbf{F}\cdot\int_{\textbf{r}_1}^{\textbf{r}_2}d\textbf{r}=\textbf{F}\cdot(\textbf{r}_2-\textbf{r}_1)$$