In the expression W = K
∆ , the work is the net work (the total work) done by all the forces acting
on the particle or rigid body. The net work can be calculated by finding the work done by each
force and adding the results, or by finding the net force and using it in the definition of the work.
Calculating the Work as the Force-Along-the-Path Times the Length of the Path
Consider a block on a flat frictionless incline that makes an angle θ with the vertical. The block
travels from a point A near the top of the incline to a point B, a distance d in the down-the-
incline direction from A. Find the work done, by the gravitational force, on the block.
A
θ
d
B
Fg = m
g
We’ve drawn a sketch of the situation (not a free body diagram). We note that the force for
which we are supposed to calculate the work is not along the path. So, we define a coordinate
system with one axis in the down-the-incline direction and the other perpendicular to that axis
┴
A
θ
B
Fg= mg
||
and break the gravitational force vector up into its components with respect to that coordinate
system.
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