After reviewing the progress of our lab reportage, We worked on Assignments 4 and 5, which have to do with vector subtraction and momentum conservation. We can use some practice thinking of momentum as a vector!
We assessed our data from yesterday. A few wanted to collect new, better data, but most were pleased with yesterday's data. Furthermore, we took a few swings at Assignments 3 and 4.
We tried our hand at tracking the motion of two lab carts that "explode" apart. Our goal was to figure out if the two carts received equal and opposite impulses.
We turned in Assignment 2 today and received Assignment 3, Assignment 4, and Assignment 5. Assignment 3 will be due tomorrow. Assignments 4 and 5 will be due on Friday.
The big agenda for tomorrow is a lab that deals with momentum changes of two lab carts as they push each other apart by means of a spring plunger. In order to determine the momentum of these carts we will need to determine their masses and their velocities. In order to determine their masses, we will need a scale or balance. In order to determine their velocities we will use our sonic rangers (aka "Motion Detectors"). The soflware that will enable us to use the Motion Detectors is called Graphical Analysys and is available for free at the links provided below: SOFTWARE FOR DATA COLLECTION ("GRAPHICAL ANALYSIS") For up-to-date operating systems: www.vernier.com/products/graphical-analysis/free/ For older operating systems: https://www.vernier.com/til/13161 Other than that, we spent some time learning how to increase our social status by removing a tablecloth from a table without removing the dishes, a handy skill to have anytime! We tried to break an egg today, but found that we couldn't, so long as we made sure the egg had enough time to stop. Our egg throwers gave the egg a certain amount of momentum, which the egg had to lose upon stopping. So it took a certain amount of impulse to stop the egg, because impulse = the loss of momentum. Fortunately for the egg, there are two factors that go into the impulse, the force of the fabric stopping the egg and the time over which the fabric exerted its force. The greater the stopping time, the smaller the stopping force.
Assignment: Impulse Graphs Impulse and momentum are the names of the quantities that we will be studying. Impulse is something like "oomph!" Isaac Newton thought of momentum as the amount of motion; the more mass a moving object has, the more "motion" it has, and the more velocity an object has, the more motion it has. But two objects that have the same mass but equal and opposite velocities would together have no motion––the motion of one is cancelled out by the motion of the other. So that is a kind of intuitive way to approach momentum. IMPULSE Impulse is a way to measure the impact that an interaction between two objects has on the motions of these objects. The greater the force of interaction, the greater the impact. The longer the time of interaction, the greater the impact. It turns out that the way to find the impulse is by finding the 'area' under the force vs time plot, for example, in a plot such as the one above.
Assignment: Problems 1, 2, 3, and 4 on the reverse of our Weekly Schedule for this week. Universal Gravitation was the order of the day. We focused on Saturn and its moons. The moons of Saturn orbit with very nearly uniform circular motion, as we saw using Celestia, which has a very nice computer model of the solar system, among other things. The first question I asked was what exerted the force on Saturn's moons that keeps them in their orbits? The answer is, of course, Saturn's gravitatiional field, F = mg, where m is the mass of the moon in orbit and g is the strength of Saturn's gravitational field out where that moon happens to be. The second question was what affects how strong Saturn's gravitational field happens to be for a given moon. There are two answers to this: 1) how much mass Saturn has (more mass means a stronger field) and 2) how far from Saturn the moon happens to be (the farther away the moon, the weaker Saturn's gravitational field will be). In order to have an equality rather than a proportionality, we need a constant of proportionality. In the case of gravitation, the constant of proportionality is called G, the Universal Gravitational Constant. It equals about 6.7 x 10^-11 Nm^2/kg^2. It is the same value everywhere (so far as we can check). And finally, because we know that the only force of significance acting on the moons from Saturn's point of view is Saturn's gravitation, the net force on a moon is just Fgrav = mg. So mg = ma, which means that a = g, and the acceleration for objects in uniform circular motion is This works not just for Saturn and its moons but for any object in orbit around another object. Which brings us to the question that has been nagging you for a while now: What's going on at the center of our Milky Way galaxy? Well, this video will tell you what has been found there, and it has a lot to do with centripetal acceleration and gravitation! We watched roughly the first 20 minutes. Because the astronomers were able to determine the speeds of the stars in their orbit around the center of the Milky Way as well as their distances from the center, they could find Mcenter, the mass of whatever these stars were orbiting. The best value now is 4 million times the mass of our Sun, but as you can see in the video, it is invisible. How can you hide 4 milliion times the mass of our Sun!? There is only one answer--you can hide it in a black hole. A carefully calculated animation of what two black holes merging would look like is linked below. There would be only one "chirp", but this video repeats it a couple of times. The chirp is produced by gravitational waves passing by at a frequency we could hear, were they sound waves. One wave is produced for every orbit, so just before merging, black holes orbit each other hundreds of times a second, much faster than the slow motion video shows! Wild! We presented solutions to Chapter 5 problems 1, 2, 3, and 5.
Assignments: Spend 20–30 minutes on Assignment 1 problems. We'll tackle them tomorrow. |
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