a force F with 8N has direction vector 5i+9j-3k. the force pushes an object on a ramp in a straight line from the point (2,3,0) to the point (4,9,15), where the coordinates are measured in meters. Find the amount of work done by the force

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- February 20th 2007, 09:12 PMggwapplied work problem
a force F with 8N has direction vector 5i+9j-3k. the force pushes an object on a ramp in a straight line from the point (2,3,0) to the point (4,9,15), where the coordinates are measured in meters. Find the amount of work done by the force

- February 21st 2007, 06:17 AMtopsquark
First the displacement of the object is

(4, 9, 15) - (2, 3, 0) = (2, 6, 15)

which has a magnitude of sqrt(2^2 + 6^2 + 15^2) = 16.278820596

The magnitude of the direction vector of the force is

sqrt(5^2 + 9^2 + 3^2) = 10.723805295

The angle between the force and the displacement is

cos(t) = (5i + 9j - 3k) (dot) (2i + 6j + 15k)/(|5i + 9j - 3k|*|2i + 6j + 15k|)

cos(t) = (10 + 54 - 45)/(10.723805295*16.278820596) = 0.108838299

W = F (dot) s = |F|*|s|*cos(t) = (8 N)*(16.278820596 m)*0.108838299 = 14.174073147 J

Thus W = 14 J.

-Dan