Consider a block of mass m which slides down a smooth inclined plane of angle qas shown in figure. Let us assume the coordinate axes as shown in the figure, to specify the components of the two vectors - although the value of work will not depend on the orientation of the axes.
Now, the force of gravity, g = -mg
and the displacement is given by
= Dx + Dy + Dz
The work done by gravity is
Wg = g. = -mg .(Dx + Dy + Dz)
or Wg = -mgDy (.= 0, .= 1,.= 0)
Since Dy = yf - yi = -h
\ Wg = -mg(yf - yi) = +mgh
If the block moves in the upward direction, then the work done by gravity is negative and is given by
Wg = -mgh
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