# Power versus Work

Power versus Work

Work is defined to be the product of force over the distance it is applied. In symbols, , where is the work, is the force, and is the distance.

W=F×d

W

F

d

Power, , is work per unit time, so , where is time.

P

P=W/t

t

This Demonstration calculates the work and power needed to lift a mass through a height in time . The darkness of the blue box indicates its mass. The distance is fixed to be and , the standard SI measurement for gravity. In this situation, Newton's second law, , where is acceleration, becomes . Substituting for in the first equation gives .

m

d

t

d=10

g=9.8

F=ma

a

F=mg

F

W=mgd