How Things Work / TUNE - Fall 2017

Homework answers 1.  Discuss each of Kepler's 3 laws. See notes. 2.  At what point in its orbit is the Earth closest to the Sun? Perihelion, which is approximately January 3-4 each year. 3.  What causes seasons? Tilt of Earth's axis. 4.  What is a semi-major axis of orbit (a)? Half the longest distance across the orbital path (ellipse). 5.  What is an Astronomical Unit (AU)? Defined as the semi-major axis of Earth's orbit - roughly 93,000,000 miles - or  half the longest width across Earth's orbit.  It is close to the average distance of Earth from the Sun. New homework (not to collect) 1. Describe each of Newton's 3 laws. 2. A 0.5 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 ...

General topics for exam 1.  Be sure to review all assigned homework, blog posts and your notes. You are permitted to have a sheet of notes for this test.  I will NOT give equations. SI units (m, kg, s) - meanings, definitions velocity average vs. instantaneous velocity acceleration related motion problems using the formulas speed of light (c) - approx 300,000,000 m/s gravitational acceleration (g) freefall problems Newton's 3 laws - applications and problems Universal gravitation - the inverse square law of gravity Kepler's 3 laws - applications and problems Astronomical Unit semi-major axis of orbit Basics of orbits epicycles Galileo and his telescope weight vs. mass Weightlessness Reference frames (recall demos) Useful equations Average speed:  v  = d/t Definition of acceleration:  (Vf - Vi) / t Final speed:  Vf = a t Distance traveled:  d = 0.5 a t^2 Newton's 2nd law (Force)...

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 becomes 1/4 of its origin...

Ancient science highlights: Epicycles Precession The epicycle model: http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf The most important things to get out of this were: - Epicycles were a very useful way to (wrongly) explain why retrograde motion happened with planets. - Precession (the wobbling of the Earth) causes us to have different North Stars (or no North Star) at various points over the course of thousands of years.  Thus, star maps are not accurate after several hundred years.  However, this was not understood until the time of Newton and others. Scientific Revolution:  roughly 1550 - 1700 - notable for the introduction of widespread experimental (evidence-dependent) mathematical science. - also notable for the 150 years that it took for geocentrism to finally die - sometimes thought of as "kick-started" by the publication of Copernicus'   De Revolutionibus Orbium Celestium , in 1543 (the year of his death).  This wa...

Shooting a ball backward from a moving car: http://www.iflscience.com/physics/what-happens-when-you-fire-ball-out-cannon-travelling-opposite-way/ Penn and Teller (1986) https://www.youtube.com/watch?v=mwkmgqbYXdE Microgravity: https://www.youtube.com/watch?v=LWGJA9i18Co Links from an earlier class: https://www.youtube.com/watch?v=RvD7mFT1eT4 https://www.youtube.com/watch?v=AO-Nbpbe8Sk https://www.youtube.com/watch?v=7GRZQUN1ADQ https://www.youtube.com/watch?v=6KL9jBCnsMc https://www.youtube.com/watch?v=p-klYOgcYHg Things to remember from tonight's class demonstrations. - 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. - the ball released from the top of the hook (on the cart) still lands in the cart itself, for the same reason:  ball is moving at the same speed as the...

1.  Briefly discuss each of Kepler's 3 laws. 2.  At what point in its orbit is the Earth closest to the Sun? 3.  What causes seasons? 4.  What is a semi-major axis of orbit (a)? 5.  What is an Astronomical Unit (AU)? 6.  An object is released from rest and falls without air resistance.      a.  How fast is it moving after 3 seconds?      b.  How far will it have fallen in this time?

What does the Sun's "motion" look like from Earth? http://astro.unl.edu/naap/ motion3/animations/sunmotions. swf The epicycle model - the OLD (and very wrong) way that orbits were conceived: http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf 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, etc.) 1. Planets take elliptical orbits, with the Sun at one focus. (If we were talking about satellites, the central gravitating body, such as the Earth, would be at one focus.) Nothing is at the other focus. Recall that a circle is the special case of the ellipse, wherein the two focal points are coincident. Some bodies, such as the Moon, take nearly circular orbits - that is, the eccentricity is very small. 2. The Area Law. Planets "sweep out" equal areas in equal times. See t...

On the size of things: http://htwins.net/scale2/ http://scaleofuniverse.com/ http://xkcd.com/482/ http://xkcd.com/1331/ This is just cool. http://workshop.chromeexperiments.com/stars/ http://www.youtube.com/watch? v=8yCzzTkDSMo Jack Horkheimer, FYI.

Tonight we discuss the acceleration due to gravity - technically, "local gravity". It has a symbol (g), and it is approximately equal to 9.8 m/s/s, near the surface of the Earth. At higher altitudes, it becomes lower - a related phenomenon is that the air pressure becomes less (since the air molecules are less tightly constrained), and it becomes harder to breathe at higher altitudes (unless you're used to it). Also, the boiling point of water becomes lower - if you've ever read the "high altitude" directions for cooking Mac n Cheese, you might remember that you have to cook the noodles longer (since the temperature of the boiling water is lower). https://www.youtube.com/watch?v=E43-CfukEgs On the Moon, which is a smaller body (1/4 Earth radius, 1/81 Earth mass), the acceleration at the Moon's surface is roughly 1/6 of a g (or around 1.7 m/s/s). On Jupiter, which is substantially bigger than Earth, the acceleration due to gravity is around 2.2 time...

Woo Hoo – it’s physics problems and questions! OH YEAH!! Please complete these by next Wednesday, to be submitted for a homework grade.  Recall that all homework/quiz grades will add up to 1/4 of your total course grade. 1.  Determine the average speed of your own trip to school: in miles per hour. Use GoogleMaps or something similar to get the distance, and recall the time from your last trip.  Your answer should be in either miles per hour or kilometers per hour. 2.  What was the meter standard originally based on?  What is it now based on?  Why was a change ever made? 3.  What is the meaning of instantaneous velocity?  How can we measure it? 4.  Give a simple way to remember how fast light is. 5.  Consider an automobile starting from rest and accelerating at 4 m/s/s.  How fast will it be traveling after 5 seconds AND how far will it have traveled in this time?  (Two answers)

Bad traffic - be there a few minutes late.  Sorry!

Intro to the mathematics of motion Today, we are going to talk about how we think about speed and the rate of change in speed (usually called acceleration).  It is a bit math-y, but don't panic - we'll summarize things nicely in a couple of simple-to-use equations. First, let's look at some definitions. Average (or constant) velocity, v v = d / t That is, distance divided by time.  The SI units are meters per second (m/s). * Strictly speaking, we are talking about speed, unless the distance is a straight-line and the direction is also specified (in which case "velocity" is the appropriate word).  However, we'll often use the words speed and velocity interchangeably if the motion is all in one direction (1D). Some velocities to ponder.... Approximately.... Keep in mind that 1 m/s is approximately 2 miles/hour. Your walking speed to class - 1-2 m/s Running speed - 5-7 m/s Car speed (highway) - 30 m/s Professional baseball throw...