# Force Conversion

The motion of an aircraft through the air can be explained and described by physical principals discovered over 300 years ago by Sir Isaac Newton. Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666, when he was only 23 years old. Some twenty years later, in 1686, he presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis." The laws are shown above, and the application of these laws to aerodynamics are given on separate slides.

## Here we will first give some basic definitions:

Mechanics is the study of the way matter and forces interact with each other. Here we are concerned with macroscopic bodies, i.e., bodies that you can easily see, in the solid state.

Statics is a field within mechanics which concerns itself with forces when no change in momentum occurs. Dynamics is a field concerned with forces and matter when a change in momentum does occur.

Kinematics is a study of motion without regard to the forces present. It is simply a mathematical way to describe motion.

A force can most easily be described as a push or a pull. When a force is applied to an object, the velocity of that object changes. This change in velocity constitutes an acceleration. So, forces are tied to accelerations. Galileo and Newton were scientists who developed our understanding of forces.

When we say that there is a force on an object we mean that there is a push or a pull on the object. Some outside agent is placing this push or pull on the object. In the metric system forces are measured in units of Newtons. This unit is named after Isaac Newton. In the English system forces are measured in units of pounds. A Newton of force is much smaller than a pound of force. It takes about 4.5 Newtons to equal a force of one pound. So, if you usually state your weight in pounds, then you could figure your weight in the Newtons by multiplying those pounds by 4.5.

Forces are vectors. That is, they are quantities that have both size and direction. Forces can be symbolized with arrows, as can all vectors. The arrow in the picture below is meant to show a force with the size of 15 Newtons directed toward the left.

An understanding of vectors is essential for an understanding of physics. A vector is a quantity that has two aspects. It has a size, or magnitude, and a direction. In contrast, there a quantities called scalars that have only size.

## Vectors are usually drawn as arrows.

More than one force can act on an object at once. For example, two people could push on a book at the same time. One person could push toward the left and the other could push toward the right. In this case the two forces would act against each other.

If the force toward the left was greater than the force toward the right, then the prevailing force would be toward the left. The strength of this prevailing force would be the difference between the strengths of the two separate forces. In this prevailing force is called the net force. Basically, the word net means total.

For example, if one person pushed the book with a force of 20 Newtons toward the left, and the other person pushed the book with a force of 18 Newtons toward the right, then that the net force would be 2 Newtons in size and directed toward the left.

The above situation has been one dimensional. When the only directions considered are to the left or to the right, then the problem can be thought of as operating on a horizontal number line, usually called the x-axis. Such situations occurring along one line are called one dimensional. One dimensional problems may also be vertical. In our context here we might consider only forces that act up or down. That would be a one dimensional problem, also. It would be operating on a vertical number line, usually called the y-axis.

However, if several forces act upon one object they need not act only along one line. For example, an object could be pushed toward the right by one force and upward by another. In this case the net force would be neither simply horizontally toward the right nor simply vertically upward. It would be aimed in a slanted direction upward and to the right. Nor would the size of this net force simply be the arithmetic sum of the sizes of the two other forces. In this situation one would use vector mathematics to calculate the net force.