Kinetics and Dynamics: Motion and Force

Reading

• Faraday, On the Various Forces of Nature: Lecture I
• Breithaupt, Understanding Physics: Chapters 2 and 3

The Force of Gravitation (Faraday Lecture I)

Faraday begins with an apology, since he had been sick and the initial lecture was postponed, but then he turns to his purpose in holding all of his lectures: to instill a sense of wonder in his audience at the workings of nature. What he means here by "wonder" is both the feeling of awe and amazement at how nature works, but also "wondering about" how it works. He wants the members of his audience, both young and old, to learn to look at the world around them with deliberate inquiry, and to begin to investigate natural phenomena, starting with the force of gravity and working through a series of demonstrations:

• Shell-lac rod attracts paper: action at a distance.
• Formation of the Earth at a globe: gravitational power or force
• Water in the balance: it has weight, but is not as dense as the platinum weight
• Water reacting with quicklime: heat is generated — another power.
• Air under pressure (in India bladder) supports iron hundredweight: air has pressure to resist gravity.
• A pendulum also demonstrates constant gravitational force.
• Replacing falling objects with different materials: All matter attracts all other matter.
• Dissolving marble into component parts: gravity still attracts parts (acidic gas falls downward).
• Composite bodies (like shot in a bottle) falls as though it were a single mass.
• Attempting to balance a toy: balance is a matter of finding the center of gravity.
• Balancing the pail of water and stick: opposing forces result in no movement.
• Balancing cork by giving it extensions and lowering its center of gravity.
• Objects falling in air interact with the air and fall at different speeds.
• Objects falling in a vacuum fall at the same speed.

Reading Notes on Breithaupt

Many scientists are very defensive of their position and methods for looking at the universe (although even within the scientific community, there is a disagreement about the scope of science and what these methods entail), and tend to oversimplify the relationship between science and other ways of looking at the univers, including religion.

Often the defense a science takes the form of presenting historical events with a particular agenda. This is especially true when scientists and historians discuss the position of Galileo in the church in the 17th century. Here are a couple of arguments to examine closely when reading histories of science:

1. Claim: The "medieval church" tightly controlled scientific thought and suppressed all opposition. Although scientists like Jim Breithaupt often point to the fact that the Bishop of Paris, Etienne Tempier, issued condemnations in 1277 that forbade academic debate supporting the Aristotelian positions that the earth was eternal and that the universe was finite, they seldom mention that these restrictions applied only to the University of Paris and only for about 10 years until they were rescinded in 1290. At other universities in France, and throughout Europe at the time, students at universities were able to discuss not only Aristotle, but the somewhat more controversial theories of Averroes. Some historians believe that these restrictions actually supported those who thought Aristotle was wrong, so that they could consider alternative theories which ultimately led to the Scientific Revolution. It is worth noting that most of these universities was supported by church foundations; if it had not been for the contributions in support of the church, there would've been no "academic science" during this period.
2. Claim: Copernicus waited until his deathbed to publish his heliocentric theory. Copernicus actually published several works, including the Commentariolus (1514), which contained a summary of his heliocentric system. He received some adverse criticism from other astronomers, such as Tycho Brahe, who pointed out (correctly) that if the Earth moved in space, we should be able to observe a phenomenon called stellar parallax, but at the time, no one could show stellar parallax for any stars. Although Copernicus had worked out the mathematical explanations for each of the planets by 1532, he resisted pleas from his friends to publish, because he still had no observational proof to support his theories. It should be noted that as far as we can tell, Copernicus made no observations of his own.
3. Claim: Copernicus' system was simpler than Ptolemy's and eliminated many of the circles requires to explain the motion of the planets. In fact, Copernicus still based his calculation on perfect circles, so he had to use epicycles to explain the variation in planetary speeds for each planet, including the Earth. His system was nearly as complex as Ptolemy's, and did not give notably better predictions for planetary positions. The real revolution leading to simplicity lies in Kepler's recognition that planets follow elliptical paths around the sun.
4. Claim: The Catholic Church was authoritarion and rigid in suppressing Galileo. There is actually considerable controversy over what actually happened with Galileo. By 1600, the Reformation was threatening the political hold of the Holy Roman Emperor, who received his authority to rule from the Pope. Copernicus' theories were published not only in the Commentariolus (which actually had little circulation among Copernicus' close friends) but also in Georg Rheticus' Narratio Prima. Rheticus worked with Copernicus to put this work together, and it accurately reflects Copernicus' heliocentric claims, but it introduced a new dimension to the debate: Rheticus was a Protestant and a friend of Martin Luther's close associate, Philipp Melanchthon. [In fact, Melancthon and Luther thought the Copernican theory foolish at best, pernicious at worst.]

This is not meant to be an exhaustive history of the reception of the Copernican heliocentric, but only a small attempt to point out that science and religion (which often means religious institutions) in the 16th and 17th centuries had a complex relationship. One cannot infer from a single event (the condemnation of Galileo) that all Europeans agreed with the Roman Curia in its actions, or that even all members and officials of the Catholic Church were in sympathy with the condemnation (they were not). Despite Galileo's condemnation, the 17th century saw many scientific achievements, including Harvey's discovery of the closed circulator system (which depended on Galileo's work in hydraulic mechanics), Hooke's discovery of the cell (which depended on an "inverted" telescope — the microscope), Nicholas Steno's work on sedimentation (which would lead to far more controversy on the age of the Earth), and Roemer's measurement of the speed of light, using observations of the four moons of Jupiter that Galileo discovered.

Key Points: The Study of Motion

Distance and Displacement, Speed and Velocity, Acceleration

Physicists use two kinds of values to talk about certain concepts: scalars and vectors. Scalar values, like distance and speed, have magnitude. Vector values have magnitude and direction.

Distance is a measure of space. Displacement is a measure of position. If in one hour you walk northwards for one mile, eastwards for one mile, and southwards for one mile, you have covered a distance of three miles, but your displacement is only one mile (eastward) of your origin. Your speed is distance/time or 3 miles/1 hour, but your velocity is displacement/hour, or 1 mile/hour.

Acceleration is change in velocity/time, so it is always a vector, with direction. This can be in the same direction as velocity, in which case your velocity increases. If acceleration is in the direction opposite to velocity, then the change in velocity is negative: it decreases. (Some people might call this deceleration).

We can talk about average velocity or average acceleration, the change in displacement over time, or the change in velocity over time. Another key idea is instantaneous velocity: the velocity (speed and direction) that an object has at a given moment. Newton invented his methods of calculus invented largely to help determine instantaneous velocity for situations where velocity is constantly changing or undergoing acceleration.

• How does abstraction help physicists understand a concept that involves a physical entity, like mass or distance?

Newton's Laws of Motion

First Law: Inertia

Aristotle, Galileo, and Newton all defined the concept of inertia, or the tendency of a body to remain in a particular state of motion or change its motion.

• Aristotle believed that certain kinds of motion were natural to certain kinds of matter. When it is free to move, earth matter (dirt, stone, metal) falls down. Water falls through air (rain), but lies on top of stones (rivers and lakes); stones sink through water. Air bubbles rise in water, and fire leaps highest of all, so the natural motions of earth matter and water are down, toward the center of the Earth, while the natural motions of air and fire are upward. Horizontal motion along the surface of the Earth, like that of an arrow, required constant force. When the arrow left the bow, it pushed the air ahead out of the way but left a partial vacuum behind. Based on the classical principle that "Nature abhors a vacuum", air rushed in to fill this developing vacuum, and pushed the arrow forward. Eventually, the resistance of the air in front of the arrow exhausted the initial impulse, the arrow stopped moving forward, the natural motion due to the wood and stone of the arrow's materials took over, and the arrow fell straight down. In this version of the concept of inertia, the force that impelled an object to move naturally came from within the object and was constantly present, and the force that caused it to move in a way contrary to its nature came from without, but had to be continuously exerted.

  

• Galileo's work with falling bodies led him to contradict Aristotle (one of the many actions that caused Galileo to be viewed as a trouble-maker) by proclaiming that bodies already in motion did not require a continuous force to remain in their state of motion. Instead, he reversed the assumption that a constant force was needed for motion to continue. Instead, his law of inertia declared that objects in motion would continue to move in a straight line at constant speed unless an outside force acted on them. In other words, force from outside is necessary to change motion; an object cannot change its own state of motion. In Galileo's definition, every kind of matter is subject to this single law of inertia; there are no "natural motions" distinct to Earth, Fire, Water, and Air.
• Newton's law of inertia takes Galileo's premise one step further. Newton does not distinguish types of matter either, but bases his claims only on the amount of matter (mass) present. He also considers that a velocity of zero is not a separate or special case. In his formulation, a body at rest will remain at rest, and a body in motion will continue in motion unless acted on by an outside force. Any change in motion in direction or speed (acceleration, even if negative in the sense that it slows the object down) requires an outside force.

  Another way to express this idea is to say that matter resists changes to its state of motion.

Second Law: The Definition of Force

The corollary to the idea that a body requires an outside force to change its state of motion and accelerate is the realization that where change in velocity or acceleration is observed, a net force must be present. Further, the amount of change depends directly on the force and inversely on the mass involved:

Δv/Δt = a = F/m.

This doesn't mean that there are no forces present where we observe lack of motion (a stationary object), or lack of change in motion (constant velocity). Rather, in those cases, the sum of all the forces acting on the object cancel each other out, and the object in in static equilibrium. The art and science of building structures is a study in the proper alignment of forces to achieve static equilibrium.

Third Law: Equal and Opposite

Newton's third law recognizes that all forces are interactions between two masses. The Earth's gravitational field pulls down a book lying on a table; the table pushes back on the book with equal but opposing force. If the forces were not equal and opposite, there would be a net force and the book would not only be moving but accelerating. The two forces acting on the book are equal and opposite, but arise from different sources.

Discussion

In the example of the book, the book is not free to move through the table: the equal and opposite forces result in a static situation. What happens when one object is free to move, for example, when you stand in tennies on the grass, and push (throw) a ball away from you? What would happen if instead you were on ice?

For Discussion:

• What are the units of displacement, velocity, and acceleration?
• What are the units of force? How is force related to motion?

---

© 2005 - 2024 This course is offered through Scholars Online, a non-profit organization supporting classical Christian education through online courses. Permission to copy course content (lessons and labs) for personal study is granted to students currently or formerly enrolled in the course through Scholars Online. Reproduction for any other purpose, without the express written consent of the author, is prohibited.