Physical Applications

Work as force through distance

Hydrostatic force

Pumping problems

The template's generality

A spring follows Hooke's law F(x) = kx. What work stretches it from x = 0 to x = s?

At what depth d below the surface does water pressure equal rho g d?

A rectangular dam panel of width W extends from the surface to depth h. What total force does the water exert?

In a pumping problem, a thin water layer at height y with cross-sectional area A(y) must be lifted a distance D(y). What is the layer's work element?

The work formula W = integral of F dx must recover W = F d for a constant force. Substituting F constant, what does the integral give?

A spring with k = 10 newtons per meter is stretched 2 meters. The work is one half k s squared. What is it in joules? Answer with a number.

The total force on a submerged vertical plate equals the pressure at its centroid times the plate's area. For a rectangle of width W and height h with top at the surface, where is the centroid?

In SI units, water's weight density rho g is approximately 9800 newtons per cubic meter. As a number, what is it? Answer with a number.

Pumping the cylindrical tank integrates rho g pi r^2 (2H - y) dy from 0 to H. The integral of (2H - y) dy over that range is what multiple of H^2? Answer like 3/2.

Force in newtons integrated over distance in meters gives work in what SI unit, one word? Answer in lowercase.