Physics 114C Mechanics Review for Final Exam Walker: Chapters 113, Emphasizing 12

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Physics 114C - MechanicsReview for Final
Exam(Walker Chapters 1-13,Emphasizing 12
13)December 5, 2008

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Physics 114C Course Evaluation

• Today we will start with a Physics 114C Course
  Evaluation, which will take 15 minutes. You are
  to rate the quality of the Lecture part of
  Physics 114 only, (not the Lab). Your
  participation is voluntary, and you may omit
  specific items if you wish. To insure
  confidentiality, do not write your name on the
  forms. Use ONLY A 2 PENCIL on the scannable
  forms. If you need a 2 pencil, raise your hand,
  and one will be provided.
• There is a remote possibility that your
  handwriting on the yellow sheets could be
  recognizable. However, this should not be of
  concern. I will not receive these results until
  after the quarter is over, and you have already
  received your course grades.
• I have selected several monitors to distribute
  and collect the forms. They will place the
  completed forms and extras in an envelope and
  return it to the Office of Educational
  Assessment. I will leave the room and return in
  15 minutes, at 245 PM, after the questionnaires
  have been completed and collected.
• I think we have had a good and productive
  quarter. Thanks for your participation!
  John Cramer

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Announcements

• Homework Assignment 9 (the last one!) is due at
  1159 PM on Saturday, December 6. Homework up to
  24 hours late will receive 70 credit. Also,
  complete the Course Survey on Tycho by December
  11.
• There are now 153/159 clicker registrations.
  For clicker credit, you must register your
  clicker by the end of the quarter, if you have
  not already done so.
• Check Tycho for your Exam 3 grades. If any of
  them are missing (or have an underline in place
  of a number), see Susan Hong (room C136 PAB)
  immediately to identify your paper and get credit
  for your work.

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The Physics 114C Final Exam

• On Tuesday, December 9, we will have the Final
  Exam, covering Chapters 1 through 13 of Walker.
  It will be a 100 point exam similar to previous
  ones, with 60 pts of multiple choice questions, a
  20 pt free-response question based on Tycho
  homework, and 20 pts of free-response qualitative
  questions. You may bring 3 note sheets to the
  Final.
• If you have successfully taken Exams 1-3 and are
  satisfied with your grades, the Final is optional
  (see the Physics 114C Syllabus for details). I
  have posted preliminary course grades on Tycho
  under Lecture Score 1.
• Final Physics 114C course grade is based 75 on
  exams and 25 on homework, plus clicker add-ons.
• The new seat assignments for the Final are now on
  Tycho.

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Lecture Schedule (Part 4)
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Chapter 12 Gravity
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Units of Chapter 12

• Newtons Law of Universal Gravitation
• Gravitational Attraction of Spherical Bodies
• Keplers Laws of Orbital Motion
• Gravitational Potential Energy
• Energy Conservation
• Tides

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Summary of Chapter 12

• Force of gravity between two point masses

• G is the universal gravitational constant

• In calculating gravitational forces, spherically
  symmetric bodies can be replaced by point masses.

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Summary of Chapter 12

• Acceleration of gravity
• Mass of the Earth
• Keplers Laws
• Planetary orbits are ellipses, Sun at one focus.
• Planets sweep out equal area in equal time.
• Square of orbital period is proportional to cube
  of distance from Sun.

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Summary of Chapter 12

• Orbital period

• Gravitational potential energy

• U is a scalar, and it goes to zero as the masses
  become infinitely far apart

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Summary of Chapter 12

• Total mechanical energy E

• Escape speed ve

• Tidal forces are due to the variations in
  gravitational force across an extended body

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Example Falling to Earth
What is the acceleration due to gravity of
an object at the altitude of the space shuttles
orbit, about 400 km above the Earths surface?
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ExampleThe Orbiting Space Station
You are trying to view the International
Space Station (ISS), which travels in a roughly
circular orbit about the Earth. If its
altitude is 385 km above the Earths surface, how
long do you have to wait between sightings?
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ExampleThe Orbiting Space Station
You are trying to view the International
Space Station (ISS), which travels in a roughly
circular orbit about the Earth. If its
altitude is 385 km above the Earths surface, how
long do you have to wait between sightings?
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ExampleThe Total Energy of a Satellite
Show that the total energy of a satellite in
a circular orbit around the Earth is half of its
gravitational potential energy.
Although derived for this particular case, this
is a general result, and is called the Virial
Theorem. The factor of ½ is a consequence of the
inverse square law.
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Chapter 13 Oscillations about Equilibrium
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Units of Chapter 13

• Periodic Motion
• Simple Harmonic Motion
• Connections between Uniform Circular Motion and
  Simple Harmonic Motion
• The Period of a Mass on a Spring
• Energy Conservation in Oscillatory Motion

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Units of Chapter 13

• The Pendulum
• Damped Oscillations
• Driven Oscillations and Resonance

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Summary of Chapter 13

• Period T time required for a motion to go
  through a complete cycle
• Frequency f number of oscillations per unit
  time
• Angular frequency w

• Simple harmonic motion (SHM) occurs when the
  restoring force is proportional to the
  displacement from equilibrium (Hookes Law).

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Summary of Chapter 13

• The amplitude A is the maximum displacement from
  equilibrium.
• Position as a function of time

• Velocity as a function of time

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Summary of Chapter 13

• Acceleration a as a function of time

• Period T of a mass on a spring

• Total energy E in simple harmonic motion

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Summary of Chapter 13

• Potential energy U as a function of time

• Kinetic energy K as a function of time

• A simple pendulum with small amplitude exhibits
  simple harmonic motion

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Summary of Chapter 13

• Period of a simple pendulum

• Period of a physical pendulum

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Summary of Chapter 13

• Oscillations where there is a nonconservative
  force are called damped.
• Underdamped the amplitude decreases
  exponentially with time

• Critically damped no oscillations system
  relaxes back to equilibrium in minimum time
• Overdamped also no oscillations, but slower
  than critical damping

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Summary of Chapter 13

• An oscillating system may be driven by an
  external force
• This force may replace energy lost to friction,
  or may cause the amplitude to increase greatly at
  resonance
• Resonance occurs when the driving frequency is
  equal to the natural frequency of the system

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Example A Block on a Spring
A 2.00 kg block is attached to a spring as
shown.The force constant of the spring is k
196 N/m.The block is held a distance of 5.00 cm
fromequilibrium and released at t 0. (a) Find
the angular frequency w, the frequency f, and the
period T.(b) Write an equation for x vs. time.
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Example A System in SHM

• An air-track glider is attached to a
  spring,pulled 20 cm to the right, and
  releasedat t-0. It makes 15 completeoscillatio
  ns in 10 s.
• What is the period of oscillation?
• What is the objects maximum speed?
• What is its position and velocity at t0.80 s?

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Example Finding the Time
A mass, oscillating in simple harmonic
motion, starts at x A and has period T. At
what time, as a fraction of T, does the mass
first pass through x ½A?
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End of Review 4

• Remember that the Final is optional. Check your
  preliminary grade on Tycho (Lecture Score 1) to
  decide if you need to take it.
• Homework Assignments 9 should be submitted
  using the Tycho system by1159 PM on Saturday,
  Dec. 6 (Tomorrow!).(24 hours late Þ 70 credit)
• Last chance to register your clicker, using the
  Clicker link on the 114C Syllabus page.