Key Equations

• Mass of a one-dimensional object
  $m={\displaystyle\int }_{a}^{b}\rho (x)dx$
• Mass of a circular object
  $m={\displaystyle\int }_{0}^{r}2\pi x\rho (x)dx$
• Work done on an object
  $W={\displaystyle\int }_{a}^{b}F(x)dx$
• Hydrostatic force on a plate
  $F={\displaystyle\int }_{a}^{b}\rho w(x)s(x)dx$

Glossary

density function

a density function describes how mass is distributed throughout an object; it can be a linear density, expressed in terms of mass per unit length; an area density, expressed in terms of mass per unit area; or a volume density, expressed in terms of mass per unit volume; weight-density is also used to describe weight (rather than mass) per unit volume

Hooke’s law

this law states that the force required to compress (or elongate) a spring is proportional to the distance the spring has been compressed (or stretched) from equilibrium; in other words, $F=kx,$ where $k$ is a constant

hydrostatic pressure

the pressure exerted by water on a submerged object

work

the amount of energy it takes to move an object; in physics, when a force is constant, work is expressed as the product of force and distance