Welcome to Physics 5 Foundations of Mechanics

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Welcome to Physics 5Foundations of Mechanics

• Prof. Meenakshi Narain
• Please come up and get a copy of the syllabus

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The smallest pieces of matter

• Particle physics is the study of smallest known
  building blocks of the physical universe -- and
  the interactions between them.
• The focus is on single particles or small groups
  of particles, not the billions of atoms or
  molecules making up an entire planet or star.

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and their large effects
Now (15 billion yrs)
Stars form (1 billion yrs)
Atoms form (300,000 yrs)
Nuclei form (180 seconds)
Protons and neutrons (10-10 s)
Domain of current accelerators 10-12 seconds
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Nature of Science

• Ptolemys geocentric universe (1st century AD,
  Alexandria)

• What is wrong with this?

• ?Contradicts observation

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Nature of Science

• Nicolas Copernicus (1473, Poland)
• Began a new scientific revolution by publishing
• De revolutionibus orbium coelestium
• (On the Revolutions of the Heavenly Spheres,
  1543)
• heliocentric model
• Agrees with observation

Book banned by Vatican until 1835
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Example Buoyancy

• Given a tub of water, it is observed that certain
  objects float on the surface, while other
  objects sink
• Caveman approach
• classify each object you find as either being a
  floater or sinker
• No predictive power, not testable, not
  disprovable
• Empirical approach
• examine many cases, look for patterns
• find wooden objects are floaters, metal objects
  are sinkers
• No real understanding of buoyancy yet
• Perhaps a pattern emerges
• Objects heavier than an equal volume of water
  sink, those lighter float
• But this only explains buoyancy
• A real theory gravitational force between objects

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What is Physics?

• Science Requires objectivity
• Science is based on experimental observation and
  quantitative meaurements
• Main objective of physics is to find the
  fundamental laws of nature
• Use them to develop theories that can predict the
  results of future experiments
• Quantitatively understand principles that
  underlie the Ultimate Question of Life, the
  Universe, and Everything
• Physics has had great success in describing what
  is known about nature using a rather small set of
  principles
• Mathematics is the language for expressing our
  theories
• Experimental results are crucial both in testing
  theoretical predictions and in uncovering new
  phenomena for which there are no theoretical
  predictions

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Physics

• Theories are more general sets of ideas from
  which the physical laws can be derived.
• For example Einsteins theory of special
  relativity is a theory and the law that nothing
  can travel faster than the speed of light follows
  from it.
• Physical laws have profound impact on chemistry,
  biology, engineering, etc. and on our daily
  lives
• no exploration of space without physics
• no cell phones/no internet
• no CAT scans and MRIs, no X rays and radiation
  therapy

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Which Physics Course Should I Take?

• Physics 3
• Less rigorous than Physics 5 minimal use of
  calculus
• Covers material most useful for premedical
  students (e.g., fluid mechanics)
• Not suitable for physics concentrators
• Physics 5
• More rigorous than Physics 3, moderate use of
  calculus
• Intended for science concentrators
• Meets requirements for physics concentration
• Physics 7
• Most rigorous introduction to mechanics,
  extensive use of calculus
• Intended for physics/science concentrators who
  have previously studied physics
• Possible to switch between Physics 5 and 7
• Physics 5/7 students take same labs
• Similar material etc.

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Course Goals

• Learn how the mechanical motion of physical
  objects can be described and predicted from a few
  basic principles
• One of the first great successes of Natural
  Science
• Understand the behavior of much that we see
  around us
• Develop an understanding of how to analyze and
  solve problems
• Identify the essential elements of a problem
• Use reasoning to find a solution
• Understanding the connection between theory and
  experiment in the sciences
• Analysis of laboratory data and errors
• Comparison with predictions
• Make connections between mechanics and other
  areas of physics / science

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Lectures

• Lectures teach the key concepts in Mechanics
• Description of underlying physics principles
• Application of principles by working out simple
  examples
• Demonstrations to illustrate the concepts
• Text
• Fundamentals of Physics 8th Edition, Vol. 1, by
  Halliday, Resnick, and Walker
• Read the chapter sections BEFORE coming to the
  class.
• Lecture schedule is posted on MyCourses.
• 5 of the grade includes
• quizzes and
• class participation (via the transmitters)

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Course Schedule
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Homework and Labs

• MyCourses web site http//www.brown.edu/mycourses
  
• post lectures, homeworks, handouts,
  announcements, etc. here
• Weekly homework assignments
• Solving homework problems is absolutely essential
  to learning physics
• Homework due at end of class on Wednesday
• (first assignment due 9/12)
• Late homework will not be accepted
• Weekly laboratory meetings
• Hands-on exploration of the concepts and
  applications of class material
• Will perform 4 project labs during the semester
• Prof. Landsberg will make lab information
  available on the web will also visit class
  shortly

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Exams and Grades

• Grading based on your homework, labs, and exam
  scores
• Homework Lowest HW score will be dropped from
  grade
• Exams
• Midterm 1 Wednesday Oct 3th, from 830-950am
• Midterm 2 Wednesday Nov 7th, from 830-950am
• Final exam on Thursday Dec 13, 9am-12pm (place
  tbd)
• Grades
• 15 discussion quizzes homework
• 20 Laboratory section.
• 5 lecture quizzes attendance via PRS
  (clickers)
• 30 exam 1 2
• 30 Final exam

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Course Help

• Conference sections that provide a less formal
  setting for answering questions and working out
  detailed examples
• TA and schedule to be announced
• Each member of the Physics 5 team will hold
  office hours to provide additional help as needed
• My office hours
• Monday, Tuesday 130 230
• Other times by appointment, or just knock - if I
  am in my office
• Office hours will be held in BH 524
• Office hours for conference section leader, lab
  supervisor will be posted in the near future
• Contact info will be posted on My Courses page
  as it becomes known
• MN narain_at_hep.brown.edu, [phone]

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Cell Phones

• Please turn OFF your cell phone.
• They disrupt the lecture!!!!

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Chapter 1

• Units
• Conversions
• Significant Figures

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Measurement

• Physics relies on quantitative measurements of
  stuff
• Length, speed, mass, etc.
• What exactly is a measurement?
• Example Harvard Bridge has a length of 364.4
  Smoots 1 ear
• Determined by laying Oliver Reed Smoot Jr. on
  bridge roadway and marking off successive lengths
• Not sure how they measured the 0.4 Smoot part
• Measurement consists of determining a physical
  quantity (length) of something (Harvard Bridge)
  in comparison to a standard (Smoot)
• Isnt a Smoot an arbitrary choice for a standard
  unit of length?
• Indeed, but so is the foot, meter, second, etc.
• Clearly, a Smoot is not the best choice to
  measure lengths in
• What if Smoot grows taller? Or isnt around when
  you need to measure something?
• We will use Système International d'Unités (SI)
  units
• Length meter (m)
• Mass kilogram (kg)
• Time second (s)

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Time

• Measurement of time based on a quantity that
  varies in a consistent manner
• Example electronic clock counts oscillations of
  an alternating voltage
• Standard unit of time 1 s 9 192 631 770
  oscillations of the light emitted by a Cesium 133
  atom
• Time is the most peculiar unit
• How do we know that time always proceeds at a
  constant rate?
• Favorite sci-fi scenario hero/villain learns how
  to slow/stop time, with everyone frozen while
  good/evil is done
• Special relativity is worth learning just to know
  how peculiar time is!!
• Time stands still if you move at the speed of
  light.
• Time goes slower in a moving reference frame.

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Length

• Meter was originally defined to be 10-7 the
  length between the north pole and equator
• For many years, the definition of a meter was set
  by the distance between markings on a particular
  platinum-iridium bar
• Standard length could be propagated by making
  bars whose length matched the standard
• Example length standard used by Prof. Eli
  Whitney Blake
• Found with 1883 note from person checking
  calibration stating Return this bar to Queen and
  Co. and demand what you paid for it
• As measurements became more precise, improved
  standards have become necessary
• Current standard 1 m is the distance traveled by
  light in 1/299 792 458 s
• Arbitrary length standard replaced by arbitrary
  choice for speed of light

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Mass

• Mass plays two roles in mechanics
• Determines an objects resistance to changes in
  its velocity
• Determines the gravitational force on the object
• As near as we can tell, an objects inertial
  and gravitational masses are identical
• This equivalence led Einstein to develop the
  general theory of relativity, from which comes
  curved space-time, black holes, an expanding
  universe

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Mass

• SI unit of mass is the kilogram (kg)
• Standard kilogram set by block of
  platinum-iridium kept in France
• Balance can be used to compare an unknown mass
  against a standard
• Example block of material will float if its mass
  is less than the mass of an equal volume of water

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Natural Units

• Speed of light relates units of length and time
• Incorporated into modern definition of length
• Example Light-year distance traveled by light
  during 1 year of time
• Quantum mechanics relates time and energy
• Energy of a photon is proportional to its
  frequency E hf
• Constant of proportionality h is called Plancks
  Constant
• Could measure time in units of inverse Joules
• Relativity relates mass and energy
• An object with mass has energy
• E mc2!
• Mass, length, and time are thus fundamentally
  inter-related
• Natural units h 2p, c 1
• Still need one arbitrary unit that sets the
  scale of all that we measure
• This is unsatisfactory

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Measurement Summary

• Physical quantities are measured in terms of
  units
• We will use SI units of m, kg, s
• Other quantities can be broken down into these
  units
• (e.g., 1 Joule 1 kg m2/s2)
• A measurement is meaningless without its units
  dont leave them out!!
• See text for extensive discussion on how to
  convert between units (e.g., 1 kg 1000 g) and
  use the proper number of significant digits

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mismatched units consequences
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Chapter 2

• Mechanics
• Motion, force, energy
• Kinematics
• How objects move
• Dynamics
• Why objects move
• The following parameters will be defined
• Displacement
  Average velocity Average
  speed Instantaneous
  velocity Average and instantaneous
  acceleration

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Motion Along a Straight Line

• We will first consider the simplest type of
  motion straight-line motion of a point-like
  object
• Straight-line motion the object moves along a
  single axis
• Example glider moving along air track
  (horizontal axis)
• Example tennis ball thrown straight up (vertical
  axis)
• Point-like object something that is vanishingly
  small
• True point-like objects (an electron, for
  example) make lousy examples
• Objects that make good examples, like a tennis
  ball, make lousy points
• Extended objects can rotate, wobble, deform, etc.
• We will simply ignore (for now) these
  complications
• Can fully characterize such motion by specifying
  an objects position as a function of time
• Position measured with respect to a coordinate
  axis aligned with the direction of motion
• Position can either be positive or negative (must
  specify origin!)

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Examples of Straight-Line Motion
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Coordinate Systems

• To specify a position, need to define a
  coordinate system
• Coordinate system specifies
• Location of origin
• Orientation of measurement axis (1D motion)
• or axes (2D, 3D motion)
• Position of an object can then be specified
  in this coordinate system
• Typically need to also define when t 0 occurs
• Location of coordinate system, starting time are
  arbitrary
• An astute choice can sometimes greatly simplify a
  problem
• Nature doesnt appear to have a preferred
  coordinate system laws of physics are the same
  in all non-accelerated coordinate systems
• This has several profound consequences more on
  this later!

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Displacement

• Suppose an object moves from position x1 to
  position x2 in a time interval Dt
• The displacement Dx is defined to be
• Displacement is positive if the position
  coordinate is increasing with time, negative if
  decreasing

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• A car drives from point 1 to point 2. After it
  arrives at its destination, its displacement is

• (1) Greater than or equal to the odometer reading
• (2) Always greater than the odometer reading
• (3) Always equal to odometer reading
• (4) Smaller than or equal to the odometer
  reading
• (5) Always smaller than the odometer reading

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Average Velocity and Speed

• Average velocity is the velocity calculated for a
  finite Dt
• Speed is the magnitude of the velocity without
  reference to direction
• Average velocity and average speed can be quite
  different

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Velocity

• The velocity v is defined to be
• Displacement velocity are positive if the
  position coordinate is increasing with time,
  negative if decreasing

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Velocity of Straight-Line Motion
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Velocity

• Average velocity vs instantaneous velocity

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Acceleration When Velocity Changes

• Example ball rolling down inclined track
• For a fixed Dt, increasing Dx
• Example ball tossed upward
• Velocity starts out positive, slows to 0, and
  then becomes increasingly negative
• Suppose the velocity changes from v1 to v2 in a
  time Dt
• The acceleration a is defined to be

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Acceleration of Straight-Line Motion
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Acceleration
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0-100 mph in 12 seconds
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• The graph shows the position as a function of
  time for two trains running on parallel tracks.
  Which is true?

position
time
t

• at time t both trains have the same velocity
• both trains speed up all the time
• both trains have the same velocity at some time
  before t
• somewhere on the graph both trains have the same
  acceleration

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• you are throwing a ball straight up in the air.
  At the highest point, the balls

• velocity and acceleration are zero
• velocity is nonzero but its acceleration is zero
• acceleration is nonzero but its velocity is zero
• velocity and acceleration are both nonzero

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Position, Velocity, and Accel. Examples
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Going Backwards

• Suppose you know v(t), what is x(t)?
• Suppose you know a(t), what is v(t)?
• Note presence of constants x0, v0
• Values depend on initial conditions

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Near-term Roadmap

• Look at case of straight-line motion with
  constant acceleration in some detail
• Introduce Vectors, which will be used to
  describe position, velocity, acceleration, etc.
  in 3 dimensions
• Vectors have both a magnitude and direction!
• Extend what we learn about straight-line motion
  to 3 dimensions

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Announcements

• First homework assignment posted on WebCT page
• Should be on the Homework page on the course
  menu area
• Please let me know if it isnt there!!
• HW due Wednesday, September 12 at end of lecture
• Late homework cannot be accepted
• Stop by or send e-mail, if you have questions or
  need help with some aspect of the course
• Biggest problem waiting too long before seeking
  help

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Collaboration Dos and Donts

• Studying with someone else can be a great way to
  learn physics
• Examples of collaboration we encourage
• Getting together with others to figure out how to
  solve HW problems
• Working with your lab partner to devise and carry
  out your lab projects
• Holding a study group to prepare for an exam or
  go over the course material
• There is a difference between collaborating and
  copying
• Examples of copying that are prohibited
• Copying someone elses homework assignment
• Incorporating parts of your partners lab report
  into your own
• Not doing your own analysis of lab data
• If in doubt, ask for clarification!!

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• A person initially at point P stays there a
  moment, then moves to Q and stays there a moment.
  She then runs quickly to R, stays there a moment,
  and then strolls slowly back to P. Which position
  vs time graph correctly represents this motion?

Q
R
P
position
position
position
position
time
time
time
(2)
(1)
(3)
position
position
position
time
time
time
(5)
(4)
(6)