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Physics Chapter 1 Part 1
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    Physics Chapter 1 Part 1 Physics Chapter 1 Part 1 Presentation Transcript

    • Chapter 1
      Conservation of mass & energy
    • Symmetry
    • Physicists usually define symmetry as invariance under transformation
      Basically, an object or system is called symmetric
      when you observe it from a different perspective
      And it remains unchanged
      Triangle
      Rotation
      Triangle
    • Most often we think of symmetry in terms of patterns or shapes
    • We encounter symmetry of translation, reflection, and rotation all around us…
      Translational
      symmetry
      Rotational
      symmetry
      Reflectivesymmetry
    • The most obvious kind of isometry is called a translation, and amounts to just pushing an object in a straight line to a new location:
      There is not a fixed point
    • another very familiar kind of isometry is rotation:
      Translations have no fixed points at all, while rotations have exactly one (called a pivot point, around which everything rotates doesn't move at all.
    • Reflections are isometries that have infinitely many fixed points.
    • The least well-known kind of isometry is usually called a glide reflection. It is a kind of cross between a reflection and a translation:
    • if we consider both orientation and fixed point behavior, each type of isometry has a unique character:
    • What kind of symmetrydo you find with a
      Checkerboard?
    • The laws of nature are also symmetrical
      With respect to translation
      Whether you perform an experiment in New York or Los Angeles, at the other edge of the Milky Way or in a galaxy a billion light-years from here, you will be able to describe the results using the same laws.
      With respect to rotation
      The laws look precisely the same whether we make measurements from the bottom, top, sides, etc. - physics has no preferred direction in space.
    • With respect to reflection
      The laws of physics are the same in a right-handed system of coordinates as in a left-handed system
      With respect to time
      The laws work exactly the same in experiment today as they did on an experiment performed yesterday or last year.
    • One of Einstein’s main goals in his explanation of general relativity was to formulate a theory in which the laws of nature would look precisely the same to all observers. In other words, the laws had to be symmetrical under any change in our point of view in space and time
    • Conservation Laws
      the word conserve does not have its usual meaning of trying not to waste something.
      The word “conserve” in physics means that a
      particular measurable property of a closed
      system does not change with time
      Thus, a conserved quantity is something that you wouldn't be able to get rid of even if you wanted to.
    • Since the total momentum in the system stayed the same, the momentum was
      “conserved”
    • Conservation of
      Angular Momentum:
      The total angular
      momentum of the
      system is constant.
      Conservation of Energy:
      the total energy of the system is constant.
      Conservation of
      Momentum:
      the mass times the
      velocity of the center of mass is constant.
    • Symmetry & the Laws of Physics
      The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system
    • Noether’s theorem states that each symmetry of a physical system implies that some physical property of that system is conserved.
      Conversely…
      Each conserved quantity has a corresponding symmetry
    • Everyone is familiar with energy but no one knows exactly what energy actually is
      For our purposes we will define Energy asthe measure of the ability to generate motion.
      A system that has energy has the ability to do work (motion in action).
      Energy is measured in the same units (joules) as work because energy is transferred during the action of work.
    • The SI unit of energy is the joule, J, (rhymes with cool), named after the British physicist James Joule.
      One Joule is the amount of energy required in order to heat 0.24 g of water by 1 °C. (The number 0.24 is not worth memorizing.)
    • Energy comparisons
    • Energy appears in different forms such as mass, heat, or motion
      Energy can travel in different ways such as light,
      sound, or electricity
      The workings of our universe—including all of our
      Technology—can be viewed from the perspective
      of energy flowing from one place to another and
      changing back and forth from one form to the next
    • Physics Fundamental Principle:
      Conservation of energy
      The total energy of a closed system always remains constant.
      Energy cannot be created or destroyed, but only transferred from one system to another
    • What is a system?
      A ‘system’ just means a group of objects that can be treated as a single unit.
      Example: our solar system
    • The law of Conservation of energy has many implications such as…
      Your car will not run forever on one tank of gas
    • Don’t we create energy at a power plant?
      No, we simply transform energy at our power plants
    • You can harness the same
      energy at home!!
    • Energy in the form of mass
      Einstein showed that mass itself could be converted to and from energy, according to his celebrated equation E = mc2, in which c is the speed of light.
      Thus we can view mass as simply another form of energy, and it is valid to measure it in units of joules.
      The mass of a 15-gram pencil corresponds to about 1.3 × 1015 J.
    • We get almost all of our energy from the sun
      The sun exchanges mass for energy
      through a nuclear reaction
    • Cosmic rays, however, are continually striking you and your surroundings and converting part of their energy of motion into the mass of newly created particles. A single high-energy cosmic ray can create a shower of millions of previously nonexistent particles when it strikes the atmosphere.
    • Mass can be defined from two different perspectives:
      1) Mass is the measure of the amount of matter that a body contains
      2) Mass is a measure of the inertial property of that body, that is, of its resistance to change of motion (Inertia).
    • Physics Fundamental Principle:
      Conservation of mass
      the total mass of a closed system always remains constant
    • All the physical stuff in our universe is called MATTER
    • Is Air Matter?
      What are the two criteria for matter?
      Does it take up space?
      Does it have mass?
    • WATER STATES OF MATTER
      Same for the cup of water as the iceberg
    • Are there more than3 states of matter?
      Fermionic
      condensates
    • In physics we study matter (and energy!) by
      measuring it
      Thus, many properties of matter are expressed quantitatively (associated with numbers)
      In order to understand what the numbers refer to we need to include “units”
    • Physics uses a select groupof the SI units knownas MKS (meter, kilogram, second) system
    • lengthSI unit: meter (m)
    • mass SI unit:
      Kilogram
      (kg)
    • SI unit for time: seconds (s)
      . NOTE: The short forms for SI units (such as mm for millimeter) are called symbols, not abbreviations
    • for most everyday experience
      prefixes we use are…
    • Scientific Notation
      Scientists must often deal with extremely large or small numbers
      Scientific notation is a way of expressing very large or very small numbers which are awkward to say and write.
    • We needscientificnotationforthesenumbers!
    • Writing a number in scientific notation:1)Put the decimal after the first digit and drop the zeroes2) Count the number of decimal places moved in step 13) Write as a product of the number (step 1) and 10raised to the power of the count (step 2)
      The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars.
      So we would write 200,000,000,000 in scientific notation as:
      2.0 x 1011
      This number is read as follows: "two point zero times ten to the eleventh."
    • Now we try a number that is very small.
      Change 0.000000902 to scientific notation
      The decimal must be moved behind the 9
      The coefficient will be 9.02
      The decimal moves seven spaces to the right, making the exponent -7
      Answer equals 9.02 x 10-7 
    • Examples
      Write each of the following numbers in scientific notation:
      (a) 93,000,000
      (b) .00005144
      (c) -33,452.8
    • Changing numbers from scientific notation to standard notation.
            Change 6.03 x 107 to standard notation.
      we can simply move the decimal seven places to the right because the exponent is 7.
      So, 6.03 x 107 = 60 300 000
    • Now let us try one with a negative exponent.
      Ex.2 Change 5.3 x 10-4 to standard notation.
      The exponent tells us to move the decimal four places to the left.
      so, 5.3 x 10-4 = 0.00053
    • Express in standard form:
      1.  1.09 x 103 
      2.  4.22715 x 108
       
      3.  3.078 x 10-4
       
      4.  9.004 x 10-2
       
      5.  5.1874 x 102 (This can be tricky!)
    • Answers:
      1) 1090
      2) 422,715,000
      3) 0.0003078
      4) 0.09004
      5) 518.74
    • Scientific certainty
      Precision
      Accuracy
      Precision indicates how close together or how repeatable the results are. 
      Accuracy indicates how close a measurement is to the accepted value.
      Accurate
      Inaccurate
    • PRECISION AND ACCURACY -- Quiz
      Consider the data obtained for the length of an object as measured by three students. The length is known to be 14.54 cm. Which of the conclusions summarizes the data?
      Trial #1 #2 #3 #4 #5 Student A 14.8 14.1 14.5 14.6 14.2Student B 14.8 14.2 14.6 14.5 14.8Student C 14.6 14.5 14.5 14.4 14.6
      a)   Student A has done the most precise work and student C the most accurate.b)   Student C has done the most precise and accurate work.c)   Student C has done the most precise work and student A the most accurate.d)   Student C has done the most precise work and student B the most accurate.e)   Student B has done the most precise work and student C the most accurate.
    • Significant figures
      All digits of a measured quantity are called significant figures
    • Scientific uncertainty
      all measurements contain some uncertainty. Such data is reported in significant figures to inform the reader of the uncertainty of the measurement. We record all significant figures unto the first uncertain number.
    • Dimensional analysis
      (also known as the factor-label method or unit-factor method)
      Whatever you measure, you have to use units
      Why is this important?
    • Example 2: If you are going 50 miles per hour, how many feet per second are you traveling?
    • We will use dimensional analysis on every physics problem we attempt to solve this year
      Remember the “joule”, the unit for energy?
    • End of unit 1 part 1