Physics

Chapter 3. How Things Move: Galileo Asks the Right Questions

The chapter’s objectives and major topics:

• continuation of the scientific process story line

• Aristotelian physics, and its difficulties

• Galileo and the experimental method

• the Law of Inertia

• velocity and acceleration

• falling objects

The opening quote

Let’s consider the opening quote: “I do not feel obliged to believe that the same God who has endowed us

with sense, reason, and intellect has intended us to forgo their use.” — Galileo Galilei

One of my favorite stories, which may be true:

Galileo was a devout catholic. One day during morning prayers while a medical student at the University of Pisa, he watched the lamplighters light the sanctuary lamps that were suspended from the high ceilings of the cathedral. He noticed the lamps sway to and fro after being lit, and he made a curious observation: the time it took for the lamps to make one full swing (the period) was the same for lamps of equal length, regardless of the distance traversed during the swing (which is four times the amplitude).

He returned to his dormitory room and began experimenting with simple pendula (a simple pendulum is a string with a mass attached at the end) and realized that the period of the motion depends only on the length of the string, not on the mass attached to the end or the amplitude of the motion. (Of course, this becomes more obvious in the absence of resistive forces such as friction.)

From that day forward, — Galileo became something of a rebel of his time, distinguishing between knowledge through experimentation and wisdom through philosophy and religion.

By the way, further experimentation has shown us that the motion of a simple pendulum depends only on the length of the string and the acceleration due to gravity, which depends on your location on Earth and, more generally, in the Universe. It has also shown us that more complex pendula and pendular motions are fascinating! For example, the Foucault pendulum has enabled us to study the rotation of the Earth.

A note on chapters 3, 4, and 5

Chapters 3, 4, and 5 focus on Newtonian physics.

Who was Newton?

Isaac Newton was the guy who, in a story, was sitting under an apple tree when he was struck on the head by a falling apple. According to this story, in that moment he “discovered” a force now known as gravity.

We’ll spend more time thinking about Newton’s contributions to physics shortly (including definitions of velocity, acceleration, force, inertia, momentum, energy, and gravity), but for now, I just want to give you a preview.

What is Newtonian physics?

Newtonian physics (also called classical physics) provides a way to think about the motion of objects by considering momentum and energy. In short, it involves the following concepts:

• acceleration causes a change in velocity

• unbalanced forces cause acceleration

• forces always come in pairs

• objects with mass attract each other though gravitational forces

• the momentum in any interaction is conserved

A note on chapters 3, 4, and 5

Chapters 3, 4, and 5 focus on Newtonian physics.

Why do we care about Newtonian physics?

Newtonian physics describes the motions of many objects we interact with on a day-to-day basis. Here are a few earthly and extraterrestrial examples:

1. basketballs, skis, bicycles, cars, ships, planes, clouds, hurricanes, drones 2. planets, moons, meteors, satellites

And, it adequately describes a lot basic phenomena in electricity and magnetism, sound, and thermodynamics.

Moreover, the philosophical differences between the Newtonian and post-Newtonian worldviews are important for our culture (this is the essence of the second story line).

What about other cases?

Newtonian physics does not correctly describe the motion of very small particles or the motion of very fast particles.

In the image to the left, Newtonian physics works only in the upper left regime. The other three regimes are described by concepts in relativity, quantum mechanics, and quantum field theory.

The Athenians

Think of the ancient Greeks. Who comes to mind?

For most people, it’s the “Big Three” of Athenian philosophy: Socrates, Plato, and Aristotle

It’s important to know that although these three, particularly Aristotle, played a significant role in the development of science, they are not considered scientists in the modern sense of the word. They were philosophers, concerned with issues such as understanding the nature of reality, morality, and ethics.

The following notes on Plato is extra, to give context and satiate part of the curiosity you may have; it won’t be on Friday’s quiz or the final.

In his Republic, Plato presents a compelling (and quite famous) analogy to explain his view of reality. Human beings, he said, were like prisoners in a cave, watching shadows on a wall. The real world — the things making the shadows — is outside and not available to our senses. But, he said, we can know this reality through the power of reason.

The ultimate realities for Plato were things he called “forms”, which embody the pure essence of being. For example, there is a form for “circle”, and every circle we see is an imperfect representation of that perfect, ideal form.

Aristotle and Aristotelian physics

Aristotle was Plato’s student, and it was Aristotle who had the greatest impact on the development of science in ancient Greece.

From my understanding, he was an adventurous man with a powerful intellect. Interestingly, his writings more like choppy notes rather than polished works.

In a step toward the scientific process, he rejected Plato’s idea of forms in favor of studying nature directly.

In a philosophical step (not toward the scientific process), he stated that the type of motion an object undergoes depends on the inner nature of the object. In his writings, he then “identified” two categories of motion:

1. terrestrial motion 2. celestial motion

According to Aristotle:

• Terrestrial motion can be either natural or violent. For example: – A heavy object such as a rock falls because its nature compels it to seek the center of the Universe (which, to the

Greeks, was the center of Earth). This was the object’s natural motion.

– When a heavy object is thrown upward, experiences a violent motion because it has been pushed to move against its nature.

– Heavier objects fall faster because their nature seeks the center of the Universe more strongly.

• Celestial motion is uniform, circular, and eternal, governing objects such as the moon, planets, and stars.

Aristotelian physics is intuitive…

Aristotle’s ideas of motion have become known as Aristotelian physics, and these ideas dominated natural philosophy for well over a thousand years. I will tell you now that it is wrong.

If it is wrong, why was it so widely accepted?

It’s sneakily intuitive!

For example, hold a heavy book in one hand and a sheet of paper in another. Now drop both simultaneously. Which hits the ground first?

The book hits first! Just as Aristotle’s teachings predict. The book hits first, according to Aristotle, because objects with a greater amount of the “element” Earth in them seek the ground more strongly.

As another example, put a book on the floor and clear a path around it. Now shove the book. What happens?

The book comes to rest! Just as Aristotle predicted, the violent motion moved it against its natural state, but its inner nature stopped the motion.

According to Aristotle, raised objects fall towards the Earth, heavier objects fall faster, moving objects come to rest, and objects at rest remain at rest. So why is Aristotelian physics wrong?

Difficulties with Aristotelian physics…

Why is Aristotelian physics wrong?

For our purposes, let’s acknowledge three questions that Aristotelian physics cannot answer*:

1. If you throw a rock into the air, when is the violent motion overcome by the rock’s natural motion?

2. How does the rock’s natural motion overcome the violent motion?

3. If heavier objects fall faster, why do certain shapes fall faster?

For question 3, consider the example in the text regarding a sheet of paper. Given two sheets of paper of the same mass, with one crumpled into a small ball and the other perfectly flat, why does the crumpled paper fall faster?

vs.

*Aristotle’s writings could not answer many other questions, such as the concept of drafting (known to competitive cyclists) and projectile motion (known to all in ball sports).

Galileo and the experimental method

Galileo learned by combining experience with intellect and reason. For this reason, he is often referred to as the “Father of the Scientific Method” or the “Father of Modern Science”.

For him, concepts such as Aristotle’s natural and violent motions never entered the picture. In other words, for him, the Aristotelian categories were simply inappropriate when it came to describing motion.

As you know from the reading, Galileo’s careful experimentation led him to conclusions that were, indeed, very different from Aristotle’s teachings.

I want underline the importance of his methods outlined in Section 3.3 by reminding you of them here. Galileo learned about the nature of motion by:

• performing experiments, designed to test specific hypotheses

• making idealizations, of real-world conditions to eliminate side effects that obscure the main effects. When idealizations cannot be made in practicality, he used thought experiments, which, although not real, were extrapolations from his actual experiments.

• limiting the scope of inquiry by considering only one question at a time.

• using quantitative methods to better understand and predict results.

At the end of the day, Galileo used the scientific process which is the common foundation of all scientific knowledge.

The Law of Inertia

Consider a smooth ball, rolling on a smooth surface.

With his experimental methods, Galileo concluded that a smooth ball would roll for a very long distance along a smooth, horizontal surface. He realized that interactions between the ball and the surface (frictional forces) and interactions between the ball and the air (air resistance, a type of frictional force) would eventually slow the ball down.

He believed that if all frictional forces could be eliminated and the horizontal surface extended an infinite length, the ball would continue moving horizontally forever.

He also believed that if air resistance could be eliminated, then an object thrown horizontally would continue around the Earth at a constant height. This may seem crazy, but it’s more or less what the moon is doing!

This led to the Law of Inertia, which, as the text correctly states, is the foundation of Newtonian physics!

Law of Inertia In the absence of external forces, an object at rest will stay at rest, and an object in motion will continue moving in a straight line with an unchanging speed.

In junior high school, my friend Vas told me that he thought he might be able to send a golf ball across Lake Michigan if it were frozen over. He had grasped the concept of inertia!

Speed

We need two ideas to describe motion: velocity and acceleration.

Conveniently, we can define these ideas using two simple and directly measurable quantities: distance and time.

First, let’s define a quantity closely related to velocity: speed.

The (average) speed of an object is the distance it travels divided by the time it takes to travel that distance.

speed = distance traveled / time to travel

s = d/t

For example, if you drive 140 miles in 2 hours, your average speed is 70 miles per hour, or 70 mph.

If the speed of light is 300,000,000 meters per second in a vacuum, how many meters does it travel in 2 seconds? Ans: 600,000,000 meters!

(By the way, though I think many of you will agree that the math can be fun, I won’t expect any math aside from simple multiplication and division for the quizzes and final. Most of the questions will be conceptual, only one or two per test will involve math.)

Equations are just abbreviations for statements; we use them to simplify the writing. As you know, the average speed of an object is the distance it travels divided by the time it takes to travel that distance, or, more simply, s = d/t.

Velocity

Quick quiz for you: 1. Define speed. 2. What is your speed if you sprint 400 meters in 4 seconds? The answer to question 2 is inhumanly possible! The fastest speed on record for a human is 12.42 meters/second.

Velocity, as you know from the reading, has three components: a number, a unit, and a direction.

The velocity of an object is defined as the object’s speed and the object’s direction of travel.

For example, 200 meters/second would describe an object’s speed, whereas 200 meters/second north would describe it’s velocity.

I don’t want to get too caught up in the details. What I want is for you to remember that velocity tells you how fast something is moving and the direction it is moving.

We often use arrows called vectors to describe quantities that have direction. For velocity, the arrow simply points in the direction an object travels, and the longer the arrow, the faster the object moves. The figure below shows two cars moving at different velocities . . . and maybe about to crash! I hope the passengers are wearing seatbelts.

Acceleration

Acceleration is a subtle concept.

Though we do a lot of quantitative analysis in physics, the qualitative features are the most basic in science. The qualitative meaning of acceleration:

an acceleration means any change in velocity

In other words, an object is accelerated if it does any of the three following things: 1. decreases its speed 2. increases its speed 3. changes direction

Think about this the next time you drive a car. You accelerate every time your speedometer reading changes. You also accelerate every time you turn a corner or go over a hill!

Though the concepts may seem simple, re-read this page until you internalize the concept of acceleration!

Falling objects

Recall that Aristotle believed that heavier objects fall faster. This is summarized in the image below on the left.

Galileo came to a different conclusion, summarized in the image below on the right.

Don’t worry too much about the exact proportional relations (e.g., between speed and time or distance and time) discussed in Section 3.6. The take home messages are:

1. in the absence of air resistance, light objects fall as quickly as massive objects. (Objects fall at the same rate.)

2. falling objects increase their speed as they fall. (Falling objects accelerate due to gravity.)

We’re not actually sure if Galileo dropped objects from the Tower of Pisa to determine their average velocity or acceleration while falling. What we do know, is that his conclusions were correct!

Apollo 15 mission

Though we’ve verified Galileo’s conclusion that objects fall at the same rate in the absence of air resistance many times, Astronaut David Scott simultaneously dropped a feather and a hammer on the moon during the Apollo 15 mission in 1971 to see if they hit the ground at the same time.

You should watch the video! https://www.youtube.com/watch?v=-4_rceVPVSY&feature=kp

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