This module is part of a collection of modules designed to make physics concepts accessible to blind students.

See http://cnx.org/content/col11294/latest/ for the main page of the collection and http://cnx.org/content/col11294/latest/#cnx_sidebar_column for the table of contents for the collection.

The collection is intended to supplement but not to replace the textbook in an introductory course in high school or college physics.

The purpose of this module is to provide an introduction to statics, equilibrium, and forces in a format that is accessible to blind students.

In addition to an Internet connection and a browser, you will need the following tools (as a minimum) to work through the exercises in these modules:

The minimum prerequisites for understanding the material in these modules include:

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

Assume that you are standing on the surface of the earth. As I explained in an earlier module, there is a gravitational attraction between your body mass and the mass of the earth that is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the center of mass of your body and the center of mass of the earth.

What about a gas planet?

If the earth was a gas planet such as Jupiter, that gravitational attraction would probably pull your body into the inner portions of the planet and your life would probably come to an abrupt end. That would be similar to trying to stand on the surface of a lake.

Impenetrable material

Fortunately, the earth is made of rock and other relatively impenetrable material, which prevents you from being pulled into the inner portions of the earth by that gravitational attraction.

In order to prevent you from being pulled into the earth, the ground that you are standing on must push up on the bottom of your feet by an amount equal to the gravitational pull that is being exerted on your body.

Your skeleton is critical

In addition, the bones in your inner skeleton must be capable of withstanding the pull of gravity on your body to prevent your body from turning into a puddle on the surface of the earth. For example, a raw egg doesn't have an inner skeleton; it has an exoskeleton, the shell. When you break the shell over a frying pan and dump the egg out of the shell, the attraction of gravity causes it to become a puddle in the frying pan.

The push is a force

In simplified terms, a force is a push or a pull. The push that is being exerted upward on the bottom of your feet by the surface of the earth is commonly called a force.

The gravitational attraction that is trying to pull you into the center of the earth is also a force (which is often referred to as your weight).

Equilibrium

If you are standing in one spot without moving up or down, the entire system that constitutes your body and the earth is in equilibrium. This means that the upward force being exerted on the bottom of your feet by the surface of the earth is equal in magnitude and opposite in direction from the gravitational force that is trying to pull you into the earth.

An object is in equilibrium when it is not being accelerated. It may be at rest and remain at rest or it may be moving with a constant velocity and continue to move at the same velocity. If it is being accelerated, which includes changing its direction of motion, it is not in equilibrium.

Force is a vector quantity

In order for a body to be in equilibrium, the vector sum of all the forces acting on that body must be zero.

The bathroom scales

Many households in the U.S. have a device that is commonly known as the bathroom scale. We use it to determine "how much we weigh."

Assume that you walk into your bathroom and step onto the bathroom scale. To understand everything that is going on, we need to recognize that the house and the scale inside the house are also being pulled toward the center of the earth by gravitational attraction. Fortunately the surface of the earth normally exerts an upward force on the foundation of the house to prevent that from happening. The foundation exerts an upward force on the bathroom floor, and the floor exerts an upward force on the scale.

When the strength of the earth fails...

Sometimes, under some conditions, the surface of the earth fails to exert an upward force on the foundation of a house sufficient to prevent it from accelerating toward the center of the earth. I recently saw a video on the news of a house that was pulled into a sinkhole in Florida. I have seen several news videos where houses have been pulled toward the center of the earth during landslides in California.

How much do you weigh?

When you are standing on the scale, the gravitational force exerted on your body is being supported by the top surface of the scale. The top surface of the scale is pushing up with a force that is equal and opposite to the gravitational force that is trying to pull you toward the center of the earth.

The scale also has a weight

A gravitational force is also being exerted on the scale trying to pull it into the center of the earth. The floor underneath the scale is exerting an upward force on the scale equal to the combined gravitational force of you and the scale, causing you, the scale, and the floor to be in equilibrium.

Compression

These two forces, one pushing down on the top of the scale and the other pushing up on the bottom of the scale causes the scale to experience something commonly called compression. In other words, the opposing forces are trying to squeeze the scale into a puddle but the material from which the scale was constructed won't allow that to happen.

Tension versus compression

As an aside, the state that we call tension is the opposite of the state that we call compression. If you sit with all of your weight on a stool, the legs of that stool will be in a state of compression. If you sit with all of your weight in a porch swing supported by chains attached to the ceiling, those chains will be in tension.

A readout in pounds

The bathroom scale contains a mechanism that is capable of measuring the amount of compression that it is experiencing. It also contains a display mechanism that displays the amount of compression. Typically in the U.S., that compression value is converted to force and displayed in units of pounds.

The objective of the bathroom scale

The objective of the bathroom scale, therefore, is to measure the gravitational force exerted on your body (your weight) and to display that value for your pleasure or displeasure as the case may be.

Units

In the so-called English system of units that is commonly used in the U.S., the word pound is used to indicate mass and the words pound force are used to indicate force. That can be confusing.

In the International System of Units, abbreviated SI, the standard unit of mass is the kilogram, abbreviated kg, and the standard unit of force is the newton, abbreviated N.

A derived unit

As you learned in an earlier module, the SI units consist of base units and units that are derived from base units. The newton is a derived unit, which when expressed in SI base units is:

1 N = 1 kg *m/s^2

where

Knowing the relationship between the newton and its base units is important when you are evaluating an equation and need to cause the units to cancel out so as to end up with only the correct units for the result.

Conversion factor

The force that is trying to pull you into the center of the earth (your weight) can be expressed in any of the following units:

The following conversion factor can be used to convert from English units to SI units:

1 pound force = 4.44822162 newtons

To convert your weight from pounds to newtons, multiply your weight in pounds by 4.448.

To convert your weight from newtons to pounds, divide your weight in newtons by 4.448.

If your bathroom scale says that your weight is 100 pounds, a bathroom scale calibrated in newtons would say that your weight is 444.8 newtons.

The basis for your weight

You may be wondering why you weigh as much as you do (other than as a result of your appetite for sweets). As mentioned earlier, the basis for your weight is the gravitational attraction between your body mass and the mass of the earth.

The acceleration of gravity

In an earlier module, you learned that two bodies in free fall above the surface of the earth, in the absence of an atmosphere, will accelerate toward the center of the earth at the same rate, which is about 32.2 ft/sec^2 or 9.8 m/s^2.

Your weight, or the gravitational force exerted on your body, is the force necessary to cause your body to accelerate toward the center of the earth at 32.2 ft/sec^2.

Acceleration = force/mass

You also learned in an earlier module that the acceleration of an object due to an applied force is directly proportional to the force and inversely proportional to the mass of the object.

Therefore, a greater force must be applied to an object with greater mass to achieve the same acceleration. The greater your body mass, the greater must be the force that will cause your body to accelerate at 32.2 ft/sec^2 toward the center of the earth.

Your weight

That force is what we commonly refer to as your weight. The greater your body mass, the greater will be your weight.

Your body in equilibrium

If you climb out and sit on the limb of a tree, that limb must be capable of exerting an amount of upward force sufficient to cancel the gravitational force acting on your body. Otherwise, you will fall to the surface of the earth or to something between the limb and the surface of the earth that is capable of exerting that upward force..

If the limb doesn't break and you are able to sit there in comfort, the entire system including the tree, the limb, your body, and the earth will be in equilibrium.

Your body out of equilibrium

If the limb is incapable of sustaining that amount of upward force, it will break and allow you to accelerate towards the center of the earth. That means that the system is not in equilibrium.

So far, I have limited the discussion to forces that are directly attributable to gravitational attraction. I began this explanation with that limitation because the effects of gravitational force are something that most of us understand pretty well.

However, there are many other examples of force, most which involve the conversion of energy into force.

A human who lifts weights

For example, a human who lifts weight eats a diet that contains energy, commonly measured in calories. The human body has the ability to convert that energy into the contraction of muscle tissue.

When the contraction of muscle tissue is applied in just the right way, a human is capable of generating forces that overcome the force of gravity exerted on an object and lift that object from the surface of the earth, or whatever is supporting it.

Conversion of chemical energy

A chemical explosion has the ability to convert chemical energy into force and cause large rocks to break their molecular bonds and shatter into small pieces, or to cause rockets to overcome the force of gravity and accelerate into outer space, leaving the effects of the earth's gravitational field behind.

Overcoming gravity

Much energy is expended in daily life to overcome the force of gravity. For example, chemical energy is converted to force to lift large steel beams high in the air to build skyscrapers. Human caloric energy is converted to various forces to tote roofing shingles up a ladder onto a rooftop to make a house water proof. Various types of energy are converted to various forces to lift water to irrigate crops. Chemical energy is converted to various forces to cause airplanes to fly. Thermal energy is converted to various forces to cause hot-air balloons to fly.

Converting kinetic energy to force

Various weather processes cause solar energy to be converted into kinetic energy in the form of moving air (wind). The blades on a windmill convert that kinetic energy to forces that are used to pump water or to make electrical power.

When water moves from a high altitude to a lower altitude, potential energy is converted to kinetic energy. The blades on a water wheel or a turbine convert that kinetic energy into forces that are used to grind grain or make electrical power.

Conversion of energy to force

With the possible exception of gravitational force, I can't think of any kind of force that doesn't result from the conversion of some form of energy. As an engineer, I strongly suspect that even gravitational force results from the conversion of energy at some level, although that conversion may take place at the molecular or atomic level.