I know that $\text{Force} \times \text{Distance = Work}$.
But, what would be the physical meaning of $\text Force \times \text Area?$
Is such a quantity used in physics?
Answer
No, not really. The reason why force x distance is a useful quantity is because work is typically defined on a moving particle: force x distance is really a special case of $W = \int F \,dx$. In other words, the particle has to have moved for there to be work.
Because movement is only one dimensional (distance) and not 2D (area), there is no clear interpretation of what force*area is. It is obvious what I mean when I say "a particle has moved 3 cm," but it is nonsensical to say that "a particle has moved 4 square miles."
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