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
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
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