A constant force F=5i−9j−2k acts upon an object moving along a straight line from point (3, 5, 8) to point B?
A constant force F=5i−9j−2k acts upon an object moving along a straight line from point (3, 5, 8) to point (7, 3, -10).
Find the work done if the distance is measured in meters and the magnitude of the force is measured in newtons.
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The work done by F is the dot product of F with the displacement vector ds.
The displacement vector is;
ds =dxi + dyj + dzk
ds = (7-3)i + (3-5)j + (-10 - 8)k
ds = 4i -2j -18k
the work is then;
W = F dot ds = Fxdx + Fydy + Fzdz
W = (5)(4) + (-9)(-2) + (-2)(-18) = 74 J