Physics for Flerfs 4, "Motion Under the Action of Gravity"

By the time of Newton it was already known that the planets revolve around the sun, with measurements, and it was possible to predict where they would be in the future (flerfs just say "nuh-uh" but can't predict the location of planets, even if they are just "lights on the dome"). What Newton added was an explanation of why it works like that.

Starting with the First Law of Motion, since objects move in straight lines unless acted upon by a force, there must be a force acting on the planets, directed towards the Sun. The same is true of the Moon orbiting around the Earth. Newton tried various models for this force, the only one that could produce results consistent with observations was proportional to the masses of the two bodies and inversely proportional to the square of the distance between them. The equation for this is F = Gm₁m₂/r², where the m's are the masses of the two object, r is the distance between them, and G is measured by experiment, not predicted.

As it's always been measured to be the same, it's known as the gravitational constant and was first measured by Henry Cavendish in 1798 in an experiment that is often discussed in this group. Since gravity is a very weak force, it's necessary to use heavy weights as the two masses and eliminate air movement and vibrations. The book gives a measurement of G from 1942 as 6.673E-11 N m² / kg². That N stands for newton, the measurement of force in the metric system

(You've really made it in science if they don't just name the law after you, but also one of the variables in that law is measured in you's. This reminds me of how in Jewish sources, authors are sometimes referred to by the name of their book, rather than their own name, and a story about a professor who said that you may use the textbook on the final name, but he said the name of the author instead of the textbook, so one student got help from the author. For example, I've got a copy of "Bueche" in front of me right now, but if someone said you could consult Bueche (before 2015, when he passed away) it could be understood to mean either his textbook or the agent, settler, or even the person. I couldn't find that story, but I did find one of a student who was allowed to bring notes on a 3x5 card, and he did, only it was measured in feet rather than inches. I had a roommate in college who was allowed a single piece of paper, so he used a piece cut from a roll of paper that was intended for a computer plotter, which may have displayed less ingenuity than the friend in highschool who owned a photo enlarger and would make really tiny cheat-sheets. I'm not going to name you, even though I think the statute of limitations has run out)

Back to physics, once we have measured G, we can calculate the mass of the Earth. Without putting it on a scale in front of your eyes. The other values we need are the acceleration of falling objects and the radius of the Earth (thanks Eratosthenes).

Next is a section on how the laws of motion apply on an incline, but that's just trigonometry so I'm going to skip it.

Finally, projectile motion. This is for trajectories short enough for the curve of the Earth not to be noticeable. I suppose we should be glad that flerfs aren't trying to lob projectiles many miles and see where they land ...

For example, a baseball player (this reminds me of an exam I was one involved with in college, the had set up one of those "Physics for Poets" (in this school it was probably pre-laws and pre-MBAs, as pre-meds had to take standard science courses, and I didn't get an A in inorganic chemistry and the associated lab just to mess with the curve, that was just lagniappe) and there was a probability question involving playing cards and some students who got the wrong answers tried to blame it on that they didn't know how many cards were in a deck or suit) throws a ball, it is accelerated downward, and travels horizontally at a constant speed (these calculations will be simpler if the wind isn't blowing, and we can ignore friction from the air over the distances baseballs can be thrown, and this is why Superman should umpire rather than play) until it hits something.

So we use linear horizontal motion to compute the horizontal motion, and uniformly accelerated motion for the vertical part and can compute things such as how fast the ball is moving at any point, where it hits the ground, and how much time it takes until that happens.

Physics For Flerfs 3, Forces and Linear Motion

I split this up over several days, the only response I got from a flerf was "Falling in a circle.. lol", to which I responded that circular motion isn't until Chapter Eight

The Discovery of Physical Laws. No equations, just an essay. Physical laws are how we express how things behave. The purpose of research in physics is to discover them. We sometimes make mistakes, in which case we haven't discovered laws of nature, for example, Aristotle's belief that it was a law that heavier objects fall faster than light ones.

Even Galileo's law of falling bodies was incomplete, and doesn't work under conditions not available to him, but it was correct under the conditions under which he performed experiments. That's true of laws we discover, they well may be updated later on as we obtain new information.

But rarely is an accepted idea found to be entirely wrong (such as Aristotle's law of falling bodies), it usually needs to be modified to fit new discoveries, not entirely discarded. Newton was wrong about some things. So we don't accept a law because a famous scientist promoted it, but because it's been confirmed by experiment.

So Newton's first law of motion. A lab instructor may not injure a human being or, through inaction, allow a human being to come to harm. Sorry about that, I'll try again.

OK, let's try the translation of Newton's words from Latin in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) that appears in the textbook: "Every body perseveres in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed thereon". That might be a bit tightly packed, so let's take it apart.

"at rest" means not moving. If it's not moving, and nothing makes it move, it's not going to start. If it does so repeatedly, physicists will be all over it trying to figure out what made it move.

"uniform motion in a straight line" is the sort of motion described in the first two chapters. IRL things moving in straight lines will eventually slow down and stop due to friction (which will be covered later in this chapter), running into something (such as the walls of the lab room), falling off the table, hitting the ice wall (not really). But as we do an increasingly better job of reducing friction, objects travel for longer before they noticeably slow down.

What's not explained in the translated quote is "forces impressed thereon". Well since it wouldn't do to not have any equations, I went to Wikipedia and found this one, but it involves calculus, so I sneakily removed it.

Σ𝐅 = 0 ⟺ 𝐚 = 0 (the part to the left of the double-arrow was covered in my OP, it means that sum off all forces, expressed as vectors, is zero, or the forces all cancel out, there's no difference if there are no forces, or someone applies a force one one side and someone else applies an equal force on the other side, or there are dozens of forces at all different angles, but applying vector addition gives zero. The double arrow means that if the condition on the left is true, the right side will be observed, and also the other way around. The right side says that there will be no acceleration, if it's at rest it will stay at rest, if it's moving at a constant speed in a straight line, it will go on doing that).

The book goes on to the Third Law (which isn't about lab assistants from protecting the lab from harm) before the Second (which isn't about lab assistants following orders of any tenured member of faculty) but I'm not having any of that. Wikipedia's expression of it in words is also easier to understand, "the rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force." Let's simplify matters and say the mass of the object isn't changing (it's not a melting ice cube or an airplane whose mass is reducing because fuel tanks are emptying) and the equation is

𝐅 = m 𝐚

It's necessary to explain the difference between weight and mass. mass is a more fundamental property of an object than weight. If you schlep (that's a technical term) an object to the top of a tall mountain, managing not to drop it along the way, it will weigh slightly less (why? the answer will astonish you!) but it will have the same mass, as can be demonstrated by trying to move it horizontally, it will take the same force to get it to accelerate by the same amount. This could also be demonstrated by a skydiver who had enough time to perform an experiment before it is time to pull the ripcord. To convert weight into mass, you just divide by the

The Third Law states that if object A exerts a force on object B, object B also exerts an equal and opposite force on object A.

Finishing up chapter 3, the force of friction is computed as f = μN where μ is the coefficient of friction (which varies according to the substances that are rubbing against one another, there's a chart that goes from wood over snow, about 0.06 to rubber over dry concrete, 0.7 to 1.0) and N is the normal force. "Normal" here isn't using the most common definition of the word but means perpendicular -the force exerted by the object on the surface on which it is traveling (and returned by the surface according to the Third Law of Motion) is at a right angle to the motion of the object across the surface. If the surface is level and the object is being pulled or pushed straight on (in the direction that it travels) the normal force is just its weight. But if it's being pulled at an angle, say a wagon that sits 8 inches off the ground pulled by a handle or string at an angle, or the surface is inclined, you'll have to use some trigonometry to calculate it.

It should be noted that there are two types of friction, kinetic, also called dynamic (when the object is moving) and static (just before it starts to move) which is higher, you may have noticed that it takes more force to start something sliding than to keep it moving. The examples of μ were for kinetic friction and the two coefficients of friction are labeled with subscripts, μₖ and μₛ.

Terminal velocity explains why Aristotle was wrong about light objects falling, the fall of objects is opposed by air resistance, which is greater for a light object and/or one with a large surface, and it also increases as the object moves faster, so eventually the two forces will have the same value (but in opposite directions) and the object will stop accelerating but fall at a constant velocity, known as terminal velocity The textbook doesn't explain how to calculate this velocity but gives some examples, a raindrop at 25 ft/sec, a person at 250 and points out that this will depend on the shape and orientation of the object, so if you're falling out of an airplane, how fast you'll be going before the sudden stop at the end depends on whether you are falling feet (or head) first or are prone and allowing you to try that yourself would violate the First Law of Lab Instructors as previously stated. But if you want to know how to compute terminal velocity for things other than yourself or your annoying roommate, see here

Physics For Flerfs 2, Uniformly Accelerated Motion.

Average speed is defined as distance traveled (or driven, if sovcits were around when this book was written neither the author nor I had heard of them yet and the book uses them both) divided by time. Symbolically, ū = d / t. The bar above the u means that it an average - if someone traveled ten feet (are we going to stay in English units throughout the book or switch to metric at some point?) in two seconds, they didn't necessarily at 5 feet/second for the entire two seconds, but that is their average speed.

Now to velocity, the average velocity vector 𝘃̄ which is the displacement vector divided by time (we covered displacement vectors in chapter 1, see "driving 30 miles east".

If we want to measure the speed or velocity at a particular instant, and we're not Zeno, we don't find it impossible to compute it. Since we're not allowed to divide by zero (they taught you that in math class, right? Don't do that, that's where black holes come from) what we do is *almost* divide by zero, we measure the distance traveled over increasingly smaller intervals, and as ∆t (the interval) *approaches* zero in the above equations we approach an instantaneous speed.

If you want to know more about this, you probably should be taking Physics with calculus, but this textbook is for Physics without calculus.

Well now we can define acceleration (and with autocorrect we can even spell it), which happens when an object changes its velocity. It is that change in velocity divided by time, 𝗮̄ = (𝐯 - 𝐯₀) / t, where 𝐯₀ is the velocity at the start, and 𝐯 is the velocity at the end (of time t).

Since the velocities are vectors, so is acceleration. This chapter only deals with motion in a straight line, no curves or turns.

There's a long note about understanding equations instead of just memorizing them and one thing I want to mention is the suggesting there about examining the limiting form of equations, the example they give is that if acceleration is zero, 𝐯 - 𝐯₀ must also be zero, so 𝐯 = 𝐯₀. Yes, that should be obvious, and if the equations give a result that isn't, we have to reconsider whether the fault is with the equation, how we applied it, or with our sense of what is obvious.

(A joke, not in the book: A professor was notorious for leaving complicated demonstrations to the students, with no more than a remark that "It is obvious that..." One day a student interrupted. "Professor, is it really obvious that the second line follows from the first?" The professor looked at the board, wrinkled his brow, paced about the room for a few minutes, then, triumphantly said, "Why yes, it is obvious." In another version he goes back to his office for most of the class and appears breathlessly just before the class ends, with the same conclusion)

OK, now we get into dangerous territory, Galileo's observations about, um, things fall down go boom boom. (there is a hilarious video by a flerf who can't understand how gas gradients work and doesn't believe in gravity, that's something he kept shouting during the video. I think it was at a fellow flerf who was trying not to be quite as ignorant) While Aristotle thought that heavier things do that faster than lighter ones and for about two millennia that was accepted as fact (Aristotle lived 384 - 322 BCE, Galileo 1564 - 1642 CE), Galileo conducted experiments. He increased the time it takes objects to fall by rolling spheres down a slope, we reproduced this experiment in the course where I used this book, and to quote "it is not unlikely that in you laboratory work you will perform an experiment to check his results").

For whatever reason (scientists are baffled!) things fall down at close to 32.2 feet per second squared. Or 9.8 meters per second squared. So here's a sample problem, a stone is dropped from a bridge over water It takes 3 seconds for it to hit the water's self-seeking level So a (don't worry, I'm not calling it g) is 32 ft / sec², v₀ = 0, so the distance is ½at² or 0.5 * 32 * 3 * 3, or 144 seconds (see last equation below)

To sum up, here are all of the equations in scalar form (the same thing happens with vectors but the book wrote them as scalars and I'm tired of going to the site that turns text bold.

s = v̄t (displacement is average velocity multiplied by time, This is the definition of average velocity, rearranged to have displacement on the left side of the equation instead of velocity)

v̄ = ½(v + v₀) (average velocity is the sum of the starting and ending speed divided by two)

v = v₀ + at (final velocity is initial velocity plus acceleration multiplied by time. This is the definition of acceleration, rearranged)

v² = v₀² + 2as (this one is a bit more complicated, we take the definition of average velocity (v̄, two equations above) and plug them into the average velocity equation, the first one in this comment, to get s = ½(v + v₀)t, then replace t by its value from the definition of acceleration and get s = ½(v + v₀)(v + v₀)/a and rearrange that to get v² - v₀² = 2as and then move the v₀² to the right side. Wow, all that algebra we studied turns out to be good for something.

Next time, Forces and Linear Motion

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Physics for Flerfs 1, Vectors and Balanced Forces

Because reasons, I'm a member of a group called Official Flat Earth & Globe Discussion, where flat-earthers (or people who think it's funny to pretend to be flat-earthers) post stupid things, get quickly refuted, but don't understand it, or people who've studied science write about science and the flerfs respond with laugh reactions, incomprehensible memes, quotes from Scriptue, and "nuh-uh". One of the things is that they don't just disbelieve that the Earth is a sphere (or a sphere that's slightly wider around the equator than around the poles, or even one that's slightly larger in the southern hemisphere than the northern), they also don't believe in gravity. So I decided to teach an introductory physics course there to see if they disagreed with anything else.

I only got one response to the first chapter, and it was questions about God, so I blocked the idiot. So anyway I'm going to post them on my wall too, because why not? I'll use the hashtag #PhysicsForFlerfs

So I went to find the simplest science textbook on my bookshelves, I picked Principles of Physics, F. Bueche, 2nd edition, 1972 which is for a general physics course without calculus. If I had taken physics at engineering school there would have been a higher-level course but I did my basic sciences at a liberal arts college where this is what they used.

So let's start in chapter 1, "Vectors and Balanced Forces".

An example of a vector is given as driving 30 miles east, it includes both magnitude (the 30 miles) and direction (east) as opposed to a scalar, e.g. driving 30 miles but not specifying which way. It gives several examples of vector addition, for example if someone goes 30 miles east and then 10 miles north, the Pythagorean theorem shows that they've gone the square root of 1000 miles, and drawing a scale diagram and using a protractor (not even trigonometry until a few pages later) shows the angle.

There are also examples of forces expressed as vectors. Let's leave out things we disagree about and do them on a table. If several forces are applied to an object, say it is being pulled on via strings from various directions, the total force can be computed by adding all the force vectors.

Quantities that are vectors appear in boldface, for example a force will be written as 𝐅

Now we get to to an object at rest. If all the forces on that object on a table are balanced, say one person applies a force of 10 pounds from one direction, and another does the same from exactly opposite the first, it won't move. This can be expressed in an equation, an object is at equilibrium if Σ𝐅 = 0, the Greek letter indicates "the sum of" so if all the forces add (via vector addition) to zero, the object won't move, or if it was already moving, it will continue to move as it would without those forces.