How Things Work - Spring 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 becomes 1/4 of its

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. Basic format:  multiple choice, short answer, maybe a short essay  SI units (m, kg, s) - meanings, definitions (original AND current) 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) - on earth (approx 10 m/s/s) and elsewhere (Moon, etc.) freefall problems Newton's 3 laws - applications and problems Kepler's 3 laws - applications and problems epicycles weight vs. mass Weightlessness Reference frames (recall demos) Newton:  _Principia Mathematica_, 1687 Inverse square law (discussed next class) Useful equations Average speed:  v  = d/t Definition of acceleration:  (Vf - Vi) / t Final speed:  Vf = a t Distance travel

New questions (and answers below): 1.  Discuss each of Kepler's 3 laws. 2.  At what point in its orbit is the Earth closest to the Sun? 3.  At what point in its orbit is the Earth moving fastest? 4.  What causes seasons? 5.  What is a semi-major axis of orbit (a)? 6.  What is an Astronomical Unit (AU)? 7.  Consider Jupiter.  It's orbit is 5 AU in size (roughly).  How long should it take Jupiter to orbit the Sun once?  Show how this calculation would be done. 8.  What is the period of Earth's orbit around the Sun? 9.  What is the size of Earth's orbit (in AU)? 10.  A 10-kg object is pushed on by a 200-N force.  What will be the acceleration? 11.  What is the weight of a 100-kg man? 12.  Would the answer to 3 be different if he was on the moon?  How so? 13.  Consider yourself standing on a scale in an elevator.  The scale reads your weight.  Compared to being at rest, how would the scale reading change (if at all) if the elevator were:

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 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.  What are epicycles and why are they important in the history of science? 8. Distinguish between weight and mass. 9.   What is the SI unit of force?  What is the English unit of force? 10.  How does weight depend on gravitational acceleration? 11.   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 / 0.5 = 80 m/s/s 3.  lower acceleration 4.  See notes.  Tablecloth pull, etc. 5

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 after published in 1543 (see below) - sometimes thought of as "kick-started" by the publication of Copernicus'   De Revolutionibus Orbium Celestium , in 1543 (the year of his death).  This was the first major work arguing for a heliocentric (sun-centered) universe.  Not initially a success of a book - its influence took decades to be realized (and very slowly) Galileo (1564 - 1642) and Newton (1642 - 1727) are often thought of as the central figures of the Sci Rev'n. Worth remembering about Galileo: - discoveries with his telescope (craters on the Moon, phases of Venus, moons of Jupiter, many stars in the Milky Way galaxy, sunspots, rings of Saturn) - convincing mathematical/logical argument for a Sun-centered universe (which he publ

http://www.iflscience.com/physics/what-happens-when-you-fire-ball-out-cannon-travelling-opposite-way/ https://www.youtube.com/watch?v=mwkmgqbYXdE Things to remember from tonight's class demonstrations. https://youtu.be/lbGCa5EPZhQ Thanks, Amanda! - 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 the horizontal position of the ball - continually moving forward at a constant speed (which is the same as the car).  The blue dots show the ball rising and then falling, due to gravity.  These 2 motions combine to make the mathematical curve called a parabola. - the ball released from the to

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, etc.) 1. Planets take elliptical orbi

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). First, some demos (in class).  Then, this video: 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,

Woo Hoo – it’s physics problems and questions! OH YEAH!! You will likely be able to do many of these problems, but probably not all.  Fret not, physics phriends!  We will cover all the material in class.  Do those you can.  Answers are below 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 try to recall the time from your last trip. Use your trip from home to Towson, or something that makes sense to you. If possible, do it in miles per hour AND m/s. 2. Consider an echo-y canyon. You stand 200-m from the canyon wall. How long does it take the echo of your scream (“Arghhhh! Curse you Physics!!!”) to return to your ears, if the speed of sound is 340 m/s? (Sound travels at a constant speed in a given environment.) Also, keep in mind that the sound has to travel away from AND back to the source. 3. What is the difference between traveling at an average speed of 65 mph for one hour and a constant

Acceleration, a a = (change in velocity) / time a = (v f  - v i ) / t Note that the  i  and  f  are subscripts.  The units here are m/s^2, or m/s/s. Acceleration is a measure of how quickly you change your speed - that is, it's a measure of 'change in speed' per time. Imagine if you got in a car and floored it, then could watch your speedometer. Imagine now that you get up to 10 miles/hr (MPH) after 1 second, 20 MPH by the 2nd second, 30 MPH by the 3rd second, and so on. This would give you an acceleration of: 10 MPH per second. That's not a super convenient unit, but you get the idea (I hope!). > The equations of motion Recall v = d/t.  That's usually how we calculate average velocity.  However, there is another way to compute average velocity: v = (v i  + v f ) / 2 where v i  is the initial velocity, and v f  is the final (or current) velocity.  This is the same as taking the average of two numbers, in this case, the initial

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What does the Sun's "motion" look like from Earth? http://astro.unl.edu/naap/ motion3/animations/sunmotions. swf 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.

The meaning of velocity 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 throwing speed -