11.0 - Introduction
Although much of physics focuses on motion and
change, the topic of how things stay the same í
equilibrium í also merits study. Bridges spanning
rivers, skyscrapers standing tall... None of these
would be possible without engineers having achieved
a keen understanding of the conditions required for
equilibrium. In this chapter, we focus on static
equilibrium. To do so, we must consider both forces
and torques, since for an object to be in static
equilibrium, the net force and net torque on it must
both equal zero.
The forces and masses involved in equilibrium can be
stupendous. The Brooklyn Bridge was the
engineering marvel of its day; it gracefully spans the East River between Brooklyn and Manhattan. The anchorages at the ends of the bridge
each have a mass of almost 55 million kilograms, while the suspended superstructure between the anchorages has a mass of 6 million
kilograms. Supporting those 6 million kilograms are four cables of 787,000 kilograms apiece. A five-year construction effort resulted in the
largest suspension bridge of its time, and one that over 200,000 vehicles pass over daily.
Engineers who design structures such as bridges must concern themselves with forces that cause even a material like steel to change shape,
to lengthen or contract. If the material returns to its initial dimensions when the force is removed, it is called elastic.
A tightrope walker balances forces and torques to maintain equilibrium.11.1 - Static equilibrium
Static equilibrium: No net torque, no net force
and no motion.
In California, equilibrium is achieved either by renouncing one’s possessions, moving to
a commune and selecting a guru, or by becoming extremely rich, moving to Malibu and
choosing a personal trainer.
In physics, static equilibrium also requires a threefold path. First, there is no net force
acting on the body. Second, there is no net torque on it about any axis of rotation.
Finally, in the case of static equilibrium, there is no motion. An object moving with a
constant linear and rotational velocity is also in equilibrium, but not in static equilibrium.
Let’s see how we can apply these concepts to the seesaw at the right. There are two
children of different weights on the seesaw. They have adjusted their positions so that
the seesaw is stationary in the position you now see. (We will only concern ourselves
with the weights of the children, and will ignore the weight of the seesaw.)
In Equation 2, we examine the torques. The fulcrum is the axis of rotation. Since the
system is stationary, there is no angular acceleration, which means there is no net
torque.
Let’s consider the torques in more detail. They must sum to zero since the net torque
equals zero. We choose to use an axis of rotation that passes through the point where
the fulcrum touches the seesaw. The normal force of the fulcrum creates no torque
because its distance to this axis is zero. The boy exerts a clockwise (negative) torque.
The girl exerts a counterclockwise (positive) torque. Since the girl weighs less than the
boy, she sits farther from the fulcrum to make their torques equal but opposite. In sum,
there are no net forces, no net torques, and the system is not moving: It is in static
equilibrium.
Note that in analyzing the seesaw, we used the fulcrum as the axis of rotation. This
seems natural, since it is the point about which the seesaw rotates when the children
are “seesawing.” However, in problems you will encounter later, it is not always so easy
to determine the axis of rotation. In those cases, it is helpful to remember that if the net
torque is zero about one axis, it will be zero about any axis, so the choice of axis is up
to you. However, this trick only works for cases when the net torque is zero. In general,
the torque depends on one’s choice of axis.