You have related a physic definition of power with the sociological concept of work as a means of earning a living.
Pay for Work can be related to Time, but it doesn't mean that the work has power associated with it.
It would be interesting to use symbolic logic here.
If P then Q
P = Rain
Q = Sidewalks Get Wet.
If it RAINs then The Sidewalks Get Wet
But, if doesn't mean that If Q then P.
Because the sidewalks could be Wet without Rain.
If X works Y times then = P pay
If P and Not X and Y = not work
Without pursuing the formula's here, my point is that Power can be attained without Work. Bill Gates doesn't have to work, yet he has Power and Money. As his fortune is mainly in MS stock, and it can just sit there.
Bill and Hillary Clinton had power in the White House, but when they left the WH they were 10 million dollars in debt.
Many poor people, are unemployed, yet they receive money. Retired people can be unemployed but have money, and even power.
The point is that Power can be derived from many sources not requiring work, and the same is true with wealth.
If this dn fit well, please delete it.