How Things Work - Fall 2018

Newton's take on gravity and orbits - which is the genesis of our modern conception of it, is based on: Universal Gravitation (1687, Principia) Newton's take on orbits was quite different. For him, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is: All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation: or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared. Big G = 6.67 x 10^-11, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces. This is an INVERSE SQUARE law, meaning that: - if the distance between the bodies is doubled, the force

What does the Sun's "motion" look like from Earth? http://astro.unl.edu/naap/ motion3/animations/sunmotions. swf If you follow the "motion" of the Sun throughout the year: The analemma - the "apparent" path of the Sun around the Earth So, it was believed that the Sun, stars, and planets ALL revolved around the Earth?  But there was a hitch: How did they explain the peculiar motion of Mars, etc. - where it seemed to go "backwards" (retrograde) every few months?  The epicycle model - the OLD (and very wrong) way that orbits were conceived: http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf This wrong theory lasted for nearly 2000 years - until.... Johannes Kepler, 1571-1630 Kepler's laws of planetary motion http://astro.unl.edu/naap/pos/animations/kepler.swf Note that these laws apply equally well to all orbiting bodies (moons, satellites, comets,

1. Describe each of Newton's 3 laws. 2. A 2 kg toy car is pushed with a 40 newton force. What is the car's acceleration? 3. Without calculating anything, what would be the effect (in problem 2) of increasing the mass of the car? 4. Give an example of Newton's 1st law in action. 5. Give an example of Newton's 3rd law in action. 6. Newton's "big book", what I claim is the most important non-religious book of all time is _____ and was published in _____. 7. Distinguish between weight and mass. 8.   What is the SI unit of force?  What is the English unit of force? 9.  How does weight depend on gravitational acceleration? 10.   Freefall review.  Consider a ball falling from rest.  How fast would it be moving after 4 seconds?  How far would it fall in this time? Answers: 1.  See notes. 2.  40 / 2 = 20 m/s/s 3.  lower acceleration 4.  See notes.  Tablecloth pull, etc. 5.  firearm recoil, etc. 6.  Principia Mathematica, 1687. 7

Lex. II. Mutationem motus proportionalem esse vi motrici impressae, & fieri secundum lineam rectam qua vis illa imprimitur. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both. Lex. III. Actioni contrariam semper & aequalem esse reactionent: sive corporum duorum actiones in se mutuo semper esse aequales &

Inertia and Frames of Reference   http://www.iflscience.com/physics/what-happens-when-you-fire-ball-out-cannon-travelling-opposite-way/ Great Penn and Teller clip worth a view: https://www.youtube.com/watch?v=mwkmgqbYXdE Things to remember from tonight's class demonstrations involving the ballistics cart.  A question was raised:  If you are flying in an airplane at a constant velocity, and you throw a ball straight up, will it land back in your hands (or elsewhere)? We were able to show that it lands back in the cart. https://youtu.be/lbGCa5EPZhQ - the ball shot from the cart lands in the cart, because it was moving at the same speed as the cart.  This is similar to Galileo's ship problem, or the idea of apples falling near the base of the apple tree. Now some data processing: The blue dots highlight the actual path of the ball - a parabola! This graph is a little confusing, since it shows 2 different motions.  The red dots are