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
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