Physics: Equilibrium and Stability

Equilibrium and Stability
The Earth exerts an attractive force on the mass of an object; in fact, every
small element of mass in the object is attracted by the Earth. The sum of
these forces is the total weight of the body. This weight can be considered
a force acting through a single point called the center of mass or center of
gravity. As pointed out in Appendix A, a body is in static equilibrium if the
vectorial sum of both the forces and the torques acting on the body is zero. If a
body is unsupported, the force of gravity accelerates it, and the body is not in
equilibrium. In order that a body be in stable equilibrium, it must be properly
supported.
The position of the center of mass with respect to the base of support determines
whether the body is stable or not. A body is in stable equilibrium under
the action of gravity if its center of mass is directly over its base of support
(Fig. 1.1). Under this condition, the reaction force at the base of support cancels
the force of gravity and the torque produced by it. If the center of mass
is outside the base, the torque produced by the weight tends to topple the
body (Fig. 1.1c).
The wider the base on which the body rests, the more stable it is; that is, the
more difficult it is to topple it. If the wide-based body in Fig. 1.1a is displaced
as shown in Fig. 1.2a, the torque produced by its weight tends to restore it to
its original position (Fr shown is the reaction force exerted by the surface on
the body). The same amount of angular displacement of a narrow-based body
results in a torque that will topple it (Fig. 1.2b). Similar considerations show
that a body is more stable if its center of gravity is closer to its base.
Section 1.2 Equilibrium Considerations for the Human Body

FIGURE 1.1 Stability of bodies

FIGURE 1.2 (a) Torque produced by the weight will restore the body to its original

position. (b) Torque produced by the weight will topple the body.

Equilibrium Considerations for the Human Body

The center of gravity (c.g.) of an erect person with arms at the side is at

approximately 56% of the person’s height measured from the soles of the feet

(Fig. 1.3). The center of gravity shifts as the person moves and bends. The

act of balancing requires maintenance of the center of gravity above the feet.

A person falls when his center of gravity is displaced beyond the position of

the feet.

When carrying an uneven load, the body tends to compensate by bending

and extending the limbs so as to shift the center of gravity back over the

feet. For example, when a person carries a weight in one arm, the other arm

FIGURE 1.3 Center of gravity for a person.

swings away from the body and the torso bends away from the load (Fig. 1.4).

This tendency of the body to compensate for uneven weight distribution often

causes problems for people who have lost an arm, as the continuous compensatory

bending of the torso can result in a permanent distortion of the spine. It

is often recommended that amputees wear an artificial arm, even if they cannot

use it, to restore balanced weight distribution.

Stability of the Human Body under the Action of an

External Force

The body may of course be subject to forces other than the downward force

of weight. Let us calculate the magnitude of the force applied to the shoulder

that will topple a person standing at rigid attention. The assumed dimensions

of the person are as shown in Fig. 1.5. In the absence of the force, the person

is in stable equilibrium because his center of mass is above his feet, which are

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Physics : In Biology and Medicine : Intro

Mechanics is the branch of physics concerned with the effect of forces on the
motion of bodies. It was the first branch of physics that was applied successfully
to living systems, primarily to understanding the principles governing the
movement of animals. Our present concepts of mechanics were formulated
by Isaac Newton, whose major work on mechanics, Principia Mathematica,
was published in 1687. The study of mechanics, however, began much earlier.
It can be traced to the Greek philosophers of the fourth century B.C. The
early Greeks, who were interested in both science and athletics, were also
the first to apply physical principles to animal movements. Aristotle wrote,
“The animal that moves makes its change of position by pressing against
that which is beneath it. . . . Runners run faster if they swing their arms for
in extension of the arms there is a kind of leaning upon the hands and the
wrist.” Although some of the concepts proposed by the Greek philosophers
were wrong, their search for general principles in nature marked the beginning
of scientific thought.
After the decline of ancient Greece, the pursuit of all scientific work
entered a period of lull that lasted until the Renaissance brought about
a resurgence in many activities including science. During this period of
revival, Leonardo da Vinci (1452–1519) made detailed observations of animal
motions and muscle functions. Since da Vinci, hundreds of people have
contributed to our understanding of animal motion in terms of mechanical
principles. Their studies have been aided by improved analytic techniques
and the development of instruments such as the photographic camera and
electronic timers. Today the study of human motion is part of the disciplines

of kinesiology, which studies human motion primarily as applied to athletic
activities, and biomechanics, a broader area that is concerned not only with
muscle movement but also with the physical behavior of bones and organs
such as the lungs and the heart. The development of prosthetic devices such
as artificial limbs and mechanical hearts is an active area of biomechanical
research.
Mechanics, like every other subject in science, starts with a certain number
of basic concepts and then supplies the rules by which they are interrelated.
AppendixA summarizes the basic concepts in mechanics, providing a review
rather than a thorough treatment of the subject. We will now begin our discussion
of mechanics by examining static forces that act on the human body.
We will first discuss stability and equilibrium of the human body, and then we
will calculate the forces exerted by the skeletal muscles on various parts of
the body.

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Stressed-Out Grasshoppers Can Damage the Entire Ecosystem

In the same way humans might be tempted to binge on some junk food when they're under stress, grasshoppers head for the carbohydrate-rich foods when they get scared. The difference is the grasshoppers can leave behind some big-scale problems for the environment.

A stressed grasshopper's body has less nitrogen because of the change in its diet, and microbes in the soil rely on that nitrogen to break down other material. Without the nitrogen from the grasshopper, plant parts will be broken down by microbes more slowly than usual, and without that help from the microbes, new plants will struggle to grow too.

So what freaks out grasshoppers? Well, getting eaten is pretty high on the list, and that's what researchers at the Hebrew University of Jerusalem and Yale used to test this idea. They split up two groups of grasshoppers; the unlucky group was exposed to spiders, and the other acted as the control. Understandably, the spider-exposed bugs went for the carbs. When they measured the rate of plant-decomposition in both areas, plants in the stress-free portion decomposed between 62 and 200 percent faster than their counterparts.

Researchers went one step further in the experiment, substituting fake "grasshoppers" in the soil with a mix of sugar, protein, and the organic compound found in grasshoppers' external skeletons. Even the small amount of nitrogen microbes took from the protein was enough to help out in decomposition.

If it sounds like an exterminating-bees-would-destroy-the-food-chain scenario, that's because it sort of is, researchers say. If humans, directly or indirectly, cut too many species in the area, it could mess with the balance of spiders, potentially causing problems from decreased crop production to more CO₂ in the atmosphere.

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Distillation

Distillation is the fractionate process of crude oil into light hydrocarbons (C₁ – C₄), gasoline, kerosene, diesel, petrol, and atmospheric reside. The products need to be further processed in the refinery before selling them out. However, some of the products can be sold directly.

The raw product used in the refinery distillation is crude oil, which is a mixture of hundreds hydrocarbons, with paraffins, aromatics and naphthenes.

Gasoline, petrol, diesel, kerosene, etc, are named fractions in the distillation process.

Crude oil has to be desalting before going to the distillation process. The pressure used in distillation it the atmospheric pressure (slightly above it), which gives the name of theatmospheric distillation.

There are three reasons why it is necessary to have a 1 atm pressure for the distillation process:

-We need to raise the boiling point of the light carbons in order to be able to condense the C₃ and C₄

-The uncondensed gas needs to be under sufficient pressure in order to flow to the next processing equipment

-Allow pressure drop in the column

The desalted crude oil needs to be preheated before going to the distillation column. The preheat exchangers are used to heat the crude oil before going to distillation. Usually these heat exchangers take the heat from the distillates that have just gotten off the distillation column.

The preheated crude oil is then introduced into a furnace and

heated to a temperature

approximately to 340 Celsius degrees. The unwanted products are vaporized in this phase.

The remaining crude oil is then flashed from the furnace to the flash zone in the distillation column, where the vapor and the liquid will separate. The vapor goes up to the top of the column and the liquid down to the bottom of the column. The liquid will still have some of the distillates that need to be fractionated, so they will be recuperated by the steam stripping.

After the steam stripping process, the remaining liquid is discharged from the distillation column. This final product it is also known as reduced crude. Depending on the refinery, the reduced crude oil can go to a further vacuum distillation to recover some other products, such as vacuum gas oil (VGO), bitumen, fuel oil production.

Depending of the type of crude oil, the distillation column may contain also a prefractionator to recover most of the light-ends (for the crude oils with very high percentages of light-ends).

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