Question

Work question: "Find the work done by a 10 pound force acting in the direction (1, 2) in moving an object 3 feet from (0, 0) to (3, 0). " I'm confused since this question does not have the angle. It only has the co-ordinates

Answer 1

i'll actually have to pick this up tomorrow.

Answer 2

Well, \[
W = \int \mathbf F\cdot d\mathbf r
\]In this case, force is constant with respect to distance, so we have: \[
W = \mathbf F \int d\mathbf r = \mathbf F\cdot \mathbf r
\]

Answer 3

The force is in the direction \(\langle 1, 2 \rangle\) with magnitude \(10\) lbs. We can normalize the direction to get a unit vector, and then use scalar multiplication to make it have magnitude \(10\) lbs.

Answer 4

The displacement vector is simply \(\mathbf r = \langle 3, 0 \rangle - \langle 0,0\rangle = \langle 3, 0\rangle\).

Answer 5

This means: \[
W = 10\frac{\langle 1,2\rangle}{\sqrt{\langle 1,2\rangle^2}} \cdot \langle 3,0\rangle
\]

Answer 6

So how would I figure out the final equation?