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- Herausgeber: Studium Publishing
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
- Veröffentlichungsjahr: 2018
Since birth, you've wanted to discover things. You started out by putting every available object in your mouth. Later you began asking the grownups all those "why" questions. None of this makes you unique — humans are naturally curious animals. What's unusual is that you've decided to take a physics course. There are easier ways to satisfy a science requirement, so evidently, you're one of those uncommon people who has retained the habit of curiosity into adulthood, and you're willing to tackle a subject that requires sustained intellectual effort. Bravo! Contents: The Rules of the Rules A Preview of Noether's Theorem 1.3 What Are The Symmetries? Lab 1a: Scaling The Ray Model of Light Rays Don't Rust Time-Reversal Symmetry The Speed of Light Reflection Lab 2a: Time-Reversal and Reflection Lab 2b: Models of Light Lab 2c: The Speed of Light in Matter Real and Virtual Images Angular Magnification Lab 3a: Images Lab 3b: A Real Image Lab 3c: Lenses Lab 3d: The Telescope Conservation of Mass Conservation of Energy Newton's Law of Gravity Noether's Theorem for Energy Equivalence of Mass and Energy Lab 4a: Conservation Laws Lab 4b: Conservation of Energy Conservation of Momentum Translation Symmetry The Strong Principle of Inertia Momentum Lab 5a: Interactions Lab 5b: Frames of Reference Lab 5c: Conservation of Momentum Lab 5d: Conservation of Angular Momentum. The Principle of Relativity Distortion of Time and Space Combination of velocities Equivalence of mass and energy Electricity and Magnetism Electrical Interactions Newton's quest Charge and electric field Circuits Voltage, Resistance Electromagnetism Magnetic interactions Relativity requires magnetism Magnetic fields, Electromagnetic signals What's Left? Lab 7a: Charge Lab 7b: Electrical Measurements Lab 7c: Is Charge Conserved? Lab 7d: Circuits Lab 7e: Electric Fields Lab 7f: Magnetic Fields Lab 7g: Induction Lab 7h: Light Waves Lab 7i: Electron Waves
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Discover Physics
Table of Contents
Lab 1a: Scaling
Apparatus
paper and card stock
ruler
scissors
Goal
Find out whether the laws of physics have scaling symmetry.
Introduction
From Gulliver to Godzilla, people have always been fascinated with scaling. Gulliver’s large size relative to the Lilliputians obviously had some strong implications for the story. But is it only relative size that matters? In other words, if you woke up tomorrow, and both you and your house had been shrunk to half their previous size, would you be able to tell before stepping out the door? Galileo was the first to realize that this type of question was important, and that the answer could only be found by experiments, not by looking in dusty old books. In his book The Two New Sciences, he illustrated the question using the idea of a long wooden plank, supported at one end, that was just barely strong enough to keep from breaking due to gravity. The testable question he then posed was whether this just-barely-strong-enough plank would still have the just-barely-strong- enough property if you scaled it up or down, i.e., if you multiplied all its dimensions — length, width, and height — by the same number.
You’re going to test the same thing in lab, using the slightly less picturesque apparatus shown in the photo: strips of paper. The paper bends rather than breaking, but by looking at how much it droops, you can see how able it is to support its own weight. The idea is to cut out different strips of paper that have the same proportions, but different sizes. If the laws of physics are symmetric with respect to scaling, then they should all droop the same amount. Note that it’s important to scale all three dimensions consistently, so you have to use thicker paper for your bigger strips and thinner paper for the smaller ones. Paper only comes in certain thicknesses, so you’ll have to determine the widths and lengths of your strips based on the thicknesses of the different types of paper you have to work with. In the U.S., some common thicknesses of paper and card-stock are 78, 90, 145, and 200 grams per square meter.3 We’ll assume that these numbers also correspond to thicknesses. For instance, 200 is about 2.56 times greater than 78, so the strip you cut from the heaviest card stock should have a length and width that are 2.56 times greater than the corresponding dimensions of the strip you make from the lightest paper.
Galileo’s illustration of his idea.
To Think About Before Lab
1. If the laws of physics are symmetric with respect to scaling, would each strip droop by the same number of centimeters, or by the same angle? In other words, how should you choose to define and measure the “droop?”
2. If you find that all the strips have the same droop, that’s evidence for scaling symmetry, and if you find that they droop different amounts, that’s evidence against it. Would either observation amount to a proof? What if some experiments showed scaling symmetry and others didn’t?
Answers to Self-Checks for Chapter 1
Self-check A: They have 180-degree rotation symmetry. They’re designed that way so that when you pick up your hand, it doesn’t matter which way each card is turned.
