Equilibrium and Elasticity
We’ve devoted a good deal of effort to understanding why and how bodies
accelerate in response to the forces that act on them. But very often we’re
interested in making sure that bodies don’t accelerate. Any building,
from a multistory skyscraper to the humblest shed, must be designed so that it
won’t topple over. Similar concerns arise with a suspension bridge, a ladder leaning
against a wall, or a crane hoisting a bucket full of concrete.
A body that can be modeled as a particle is in equilibrium whenever the vector
sum of the forces acting on it is zero. But for the situations we’ve just described,
that condition isn’t enough. If forces act at different points on an extended body,
an additional requirement must be satisfied to ensure that the body has no
tendency to rotate: The sum of the torques about any point must be zero. This
requirement is based on the principles of rotational dynamics developed in
Chapter 10. We can compute the torque due to the weight of a body by using the
concept of center of gravity, which we introduce in this chapter.
Idealized rigid bodies don’t bend, stretch, or squash when forces act on
them. But all real materials are elastic and do deform to some extent. Elastic
properties of materials are tremendously important. You want the wings of an
airplane to be able to bend a little, but you’d rather not have them break off.
Tendons in your limbs need to stretch when you exercise, but they must return
to their relaxed lengths when you stop. Many of the necessities of everyday
life, from rubber bands to suspension bridges, depend on the elastic proper-
ties of materials. In this chapter we’ll introduce the concepts of stress, strain,
and elastic modulus and a simple principle called Hooke’s law, which helps
us predict what deformations will occur when forces are applied to a real (not
perfectly rigid) body.