The Laws of Motion: Inertia and Force

Introduction

Outline

• The Notion of Force
• Practice with the Concepts
• Discussion Points

Newton's first two laws of Motion

We have spent the last two weeks talking about kinematics, that is, the study of motion without strict attention to the forces or circumstances that give rise to that motion. This week we turn our attention to force itself and consider the questions: what is force? How does a combination of forces give rise to motion, or to a state of equilibrium?

Together with the study of motion, or kinematics, the study of forces -- dynamics -- makes up the area of physics called mechanics, which, according to Pappas of Alexandria,

examines bodies at rest, their natural tendency, and their locomotion in general, not only assigning causes of natural motion, but devising means of impelling bodies to change their position, contrary to the natures, in a direction away from their natural places.

Force

We think of force as a push or pull on an object, but in fact, the four fundamental forces of nature that we will deal with in this course are not the result of one object acting directly on another. They are properties of matter itself influencing other nearby blobs of matter. Gravitational force, electomagnetic force, and the strong and weak nuclear forces do not require contact in order to influence masses or charged particles, only proximity. The object affected only has to be near enough the gravitational mass or the charged particle producing the field for the force to result in a measurable change in movement, or, as we now understand, in an acceleration of some sort.

Back to our regular programming....

We use the concept of a "field", or region of space with certain characteristics, to help us visualize what happens because of forces that arise from blobs of matter. This idea was the product of one of the great experimentalists of all time, Michael Faraday. While his original intent was to represent graphically something for which he lacked the mathematical skills to represent in equations, Faraday's vision proved more accurate than he could have imagined. Einstein's theory of gravity rests on the concept that matter bends the space it is in, so the fields have a physical reality.

Some forces, like the Coriolis force, are apparent forces, the result of the acclerating reference frame of the observer. We see movement not because the object we observe moves in response to a force, but because we ourselves are experiencing a force. Systems involving accelerating frames of reference are beyond the scope of this course, except where we briefly consider them in our discussion of General Relativity.

But let's go back for a moment to the original question: why do objects move, and why do they change direction, speed, stop, or start? Aristotle tried to answer this by assuming that each kind of matter had a natural place toward which it moved, unless it was held back (constrained) or forced (by violent motion) to move contrary to its nature. Fire and air moved upwards, earth and water moved downwards. Therefore throwing a rock was a case of violent motion, and the rock required a constant force to keep it moving horizontally.

According to Aristotle, this force was supplied by a kind of vacuum suction push-and-pull. Air pushed out of the way in front of the projectile as it moved forward rushed in to fill the vacuum left behind the projectile. This force gradually dissipated, and when it was gone, the natural motion of the earthy-rock took over, and it fell to the ground. Heavier rocks fell faster because there was more earthy matter, and therefore more innate desire of that matter, to go down.

To some extent, Aristotle was able to convince his students of his point of view because the Greeks did not apply mathematics to physical entities the way we do now. The objects of mathematics were always abstractions: perfect lines, points, spheres, and relationships between absolute numbers. These relationships might parallel observations of a particular set of ratios between quantities in nature, but they could not be held to apply directly to the physical bodies themselves. As far as we can determine, very few of the ancient philosophers experimented with rocks and took measurements in order to confirm or disprove Aristotle's theory. We don't have any succinct arguments against it in Western European tradition until the Europeans came in contact the manuscripts of John Philoponus (a sixth century Byzantine philosopher who wrote a detailed critic of Aristotle's Physics) in the twelfth and thirteenth centuries. Philoponus took Aristotle's argument apart, but he didn't have a very extensive system to put in its place. Nonetheless, he provided food for thought to the late medieval philosophers like John Buridan who struggled with a concept of impetus -- the starting force given to a projectile -- and how it changed as the projectile moved. They paved the way for the new paradigm of matter and motion that Galileo produced at the end of the sixteenth century.

It took Galileo a lot of falling body and inclined plane rolling-body experiments to perceive one crucial point: matter does not differentially move up or down. Galileo violated the division between the disciplines of mathematics and natural philosophy, and applied mathematical analysis to the movement of real bodies, and came to a very different conclusion from that of Aristotle: All unconstrained matter moves downward toward the earth's surface at a constant rate. In separating matter into a kind that moved up and a kind that moved down, Aristotle had created a serious problem which Galileo's new assumption overcame.

But Aristotle was also partly right: bodies had a "natural" motion, which they retained unchanged unless acted upon "violently" by some outside impetus, force, push, or pull. Galileo reformed this idea to fit with his new definition of the nature of matter, and declared that all matter in motion continues in motion in a straight line, and all matter at rest, stays at rest, unless acted upon by an outside force. This concept, which we call inertia, formed the basis of Newton's new mechanics, published in Latin as the Primcipia Mathematica, or the principles of mathematical physics.

Modern physicists have established a few ground rules for analyzing situations in which forces are acting.

• First: identify the forces being exerted in a given situation. These forces can arise from fields, like gravity, or from direct pressure exerted on a body. My computer sits on a table, and it isn't accelerating. We know that there is a gravitational force pulling the computer down. But the NET force on the computer must be zero (no acceleration), so there must be one or more forces that counter this gravitational force.
• Second: identify which body each forces is acting on. In our particular case, we are interested in the computer, and the forces acting on the computer. The earth's gravity pulls the computer down, the table pushes the computer up. The computer is also pushing the table down, but the floor it pushing the table up, or it, too, would be moving.

Practice with the Concepts

Discussion Points

• A box rests on the (frictionless) bed of a truck. The truck accelerates forward and the box immediately starts to slide toward he rear of the truck bed. Discuss the motion of the box, interms of Newton's laws, as seen by an observer standing on the ground as the truck passes, and a second observer riding on the truck.

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