Calculus III Vectors - Find work done by force?

Question

Find the work done by force F = -3j (pounds) applied to distance that moves on a line from point (1,3) to (4,7). Assume distance is measured in feet. I just started learning vectors so I'm not sure if the following is correct:
Would the distance be (4-1, 7-3) = 3i + 4j?
Since W = F•D, is the answer (-3j) • (3i + 4j) = -12 foot-pounds? Thanks in advance

Don't worry about converting just leave it in foot-pounds - that's how the book does it.

The force is not in the same direction as the motion so it is not merely force times distance.

Answer 1

Your answer is correct and you argued it correctly. Remember that the Force is only in y direction so moving in x-direction requires no extra work. Think about it as a hill. Walking up requires some work, but walking on the same level of the top of the hill (if there were no friction) requires no work.

You cannot multiply the distance by the force b/c they are not at the same direction. There is cos(phi), (phi angle between Force and Distance Vector) is needed if you want to use scalar operation.

W = F•D => |W|=|F|*|D|*cos(phi)

BTW, negative work means you didn't spend any energy, instead you gain some. Let's say you ride your bicycle downhill.

Last but definitely not least: Make sure that the units are correct.

Answer 2

3i + 4j = sqrt(3^2+4^2) = 5
That is 5 feet, for this equation to work, distance must be in meters.
5 feet = 1.524 meters
-3 pounds = -13.344 Newtons

W = F*D
W = (-13.344)(1.524)
W = -20.336 Joules

Answer 3

Distance , d = 3 i + 4 j
Work done = F . d
Work done = ( - 3 j ) . ( 3 i + 4 j )
Work done = 12 ft lbs

Answer 4

do you've any suggestion about the e book that the question replaced into taken from, and if so what #. I actual have performed all this stuff yet i dont favor to apply a extra stepped ahead technique and get you in worry...

Answer 5

I always just skipped those stupid work force problems. I still got an A.