Physics 211: Lecture 1 Mechanics for Physicists and Engineers Agenda for Today

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Physics 211 Lecture 1Mechanics for Physicists
and EngineersAgenda for Today

• Course information and advice (how does the
  course work?)
• Class plus WWW
• Scope of this course
• Measurement and Units
• Fundamental units
• Systems of units
• Converting between systems of units
• Dimensional Analysis
• 1-D Kinematics (review)
• Average instantaneous velocity and acceleration
• Motion with constant acceleration

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Course Info Advice

• Go to http//www.physics.uiuc.edu and follow
  courses link to the Physics 211 homepage. This
  is always your starting point.
• Course has several components
• Discussion sections (tutorials, problem solving,
  quizzes)
• Labs (group exploration of physical phenomena)
• Homework sets, Web based
• Lecture (demos, discussion and i-clicker
  questions)
• What happens if you miss a lab or discussion
  section
• Cant make this up, will get ex or 0.
• Give excuse document to staff in 233 Loomis
• (Note from doctor or emergency dean or coach)
• The first few weeks of the course should be
  review, hence the pace is fast. It is important
  for you to keep up!

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Lecture Organization

• Three main components
• Lecturer discusses class material
• Follows lecture notes very closely
• Modified lecture notes posted each day
• Lecturer does as many demos as possible
• If you see it, you gotta believe it!
• Look for the symbol
• Students work in groups on conceptual Active
  Learning (ACT) problems and vote on the answer
  using their i-clicker.
• About 3-4 times per lecture

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Turn on your i-clicker and vote
on

• How would you best describe your high school
  physics class?
• I liked it and I remember quite a bit
• I liked it but I dont remember much
• I didnt like it but I remember quite a bit
• I didnt like it and I dont remember much
• I didnt take one

Show how to register
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Back to How Grades are Calculated

• Your final grade for Physics 211 will be based
  upon your total score on all the components of
  the course.
• The total score is the sum of your scores on the
• final exam (300 pts),
• three exams (100 pts each),
• labs (200 pts total),
• homework/quizzes/lecture (200 pts total).
• Adds to 1000
• Based on our experience from previous semesters,
  rough guidelines for letter grades (minimum
  score) this semester will be
• A(950), A(920), A-(900),
• B(880), B(860), B-(835),
• C(810), C(780), C-(750),
• D(720), D(690), D-(610),
• and F(lt610).

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Grades

• 10 labs (zero through 9) for 200 points (very
  important)
• Lecture participation (ACTS)
• 1 point per lecture maximum of 20 points.
• Everyone gets a free point for today's lecture
• 9 quizzes 14 HW(AB) - 4 lowest for 180 pts
• Where are the quizzes? Discussion section
• Where are the homework problems? On the web
• 3 midterm exams (100 pts each) for 300 pts
• One big final exam worth 300 pts

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Grades

• Notice that we do NOT use the common 90/80/70/60
  breakdown for letter grades. The reason for this
  is that for some parts of the course the average
  score is typically very high.

• Example suppose you keep up with things and
  average 95 on HW/Disc/Lab/Lect. This amounts to
  380 points out of the 1000
• What do you need on your exams, then?
• To get an A- (900) you need 520/600 0.87
• To get a B- (835) you need 455/600 0.76
• To get a C- (750) you need 370/600 0.62

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Scope of Physics 211

• Classical Mechanics
• Mechanics How and why things work
• Classical
• Not too fast (v ltlt c) relativity (325)
• Not too small (d gtgt atom) quantum mechanics
  (214, etc)
• Most everyday situations can be described in
  these classical terms.
• Path of baseball
• Orbit of planets
• etc...

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Fundamental Units

• How we measure things!
• All things in classical mechanics can be
  expressed in terms of the fundamental units
• Length L
• Mass M
• Time T
• For example
• Speed has units of L / T (i.e. miles per hour).
• Force has units of ML / T2 etc... (as you will
  learn).

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Units...

• SI (Système International) Units
• mks L meters (m), M kilograms (kg), T
  seconds (s)
• cgs L centimeters (cm), M grams (gm), T
  seconds (s)
• British Units
• Inches, feet, miles, pounds, slugs...
• We will use mostly SI units, but you may run
  across some problems using British units. You
  should know how to convert back forth.

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Converting between different systems of units

• Useful Conversion factors
• 1 inch 2.54 cm
• 1 m 3.28 ft
• 1 mile 5280 ft
• 1 mile 1.61 km
• Example convert miles per hour to meters per
  second

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Dimensional Analysis

• This is a very important tool to check your work
• Its also very easy!
• Example
• Doing a problem you get the answer distance
• d vt 2 (velocity x time2)
• Units on left side L
• Units on right side L / T x T2 L x T
• Left units and right units dont match, so answer
  must be wrong!!

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Lecture 1, Act 1Dimensional Analysis

• The period P of a swinging pendulum depends only
  on the length of the pendulum d and the
  acceleration of gravity g.
• Which of the following formulas for P could be
  correct ?

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Lecture 1, Act 1 Solution

• Realize that the left hand side P has units of
  time (T )
• Try the first equation

(a)
Not Right !!
(a)
(b)
(c)
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Lecture 1, Act 1 Solution

• Try the second equation

(b)
Not Right !!
(a)
(b)
(c)
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Lecture 1, Act 1 Solution

• Try the third equation

(c)
This has the correct units!! This must be the
answer!!
(a)
(b)
(c)
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Motion in 1 dimension

• In 1-D, we usually write position as x(t).
• Since its in 1-D, all we need to indicate
  direction is or ?.
• Displacement in a time ?t t2 - t1 is
  ?x x(t2) - x(t1) x2 - x1

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1-D kinematics

• Velocity v is the rate of change of position
• Average velocity vav in the time ??t t2 - t1
  is

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1-D kinematics...

• Consider limit t1 t2
• Instantaneous velocity v is defined as

x
so v(t2) slope of line tangent to path at t2.
x2
??x
x1
t
t1
t2
??t
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1-D kinematics...

• Acceleration a is the rate of change of
  velocity
• Average acceleration aav in the time ?t t2 -
  t1 is

• And instantaneous acceleration a is defined as

using
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Recap

• If the position x is known as a function of time,
  then we can find both velocity v and acceleration
  a as a function of time!

x
t
v
t
a
t
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More 1-D kinematics

• We saw that v dx / dt
• In calculus language we would write dx v dt,
  which we can integrate to obtain

• Graphically, this is adding up lots of small
  rectangles

v(t)

...
displacement
t
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1-D Motion with constant acceleration

• Math 220
• Also recall that
• If a is constant, we can integrate this using the
  above rule to find
• Similarly, since we can
  integrate again to get

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Recap
Ramp w/ lights

• So for constant acceleration we find

x
t
v
t
a
t
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Lecture 1, Act 2Motion in One Dimension

• When throwing a ball straight up, which of the
  following is true about its velocity v and its
  acceleration a at the highest point in its path?
• (a) Both v 0 and a 0.
• (b) v ? 0, but a 0.
• (c) v 0, but a ? 0.

y
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Lecture 1, Act 2Solution

• Going up the ball has positive velocity, while
  coming down it has negative velocity. At the top
  the velocity is momentarily zero.
• Since the velocity is
• continually changing there must
• be some acceleration.
• In fact the acceleration is caused
  by gravity (g
  9.81 m/s2).
• (more on gravity in a few lectures)
• The answer is (c) v 0, but a ? 0.

x
t
v
t
a
t
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Useful Formula 1-D motion with constant
acceleration

• Plugging in for t

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Recap
Washers

• For constant acceleration

• From which we know

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Problem 1

• A car is traveling with an initial velocity v0.
  At t 0, the driver puts on the brakes, which
  slows the car at a rate of ab

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Problem 1...

• A car is traveling with an initial velocity v0.
  At t 0, the driver puts on the brakes, which
  slows the car at a rate of ab. At what time tf
  does the car stop, and how much farther xf does
  it travel?

v0
ab
x 0, t 0
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Problem 1...

• Above, we derived v v0 at
• Realize that a -ab
• Also realizing that v 0 at t tf
• find 0 v0 - ab tf or
• tf v0 /ab

x
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Problem 1...

• To find stopping distance we use

• In this case v vf 0, x0 0 and x xf

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Problem 1...

• So we found that
• Suppose that vo 65 mi/hr 29 m/s
• Suppose also that ab g 9.81 m/s2
• Find that tf 3 s and xf 43 m

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Problem Solving Tips

• Read Carefully!
• Before you start work on a problem, read the
  problem statement thoroughly. Make sure you
  understand what information is given, what is
  asked for, and the meaning of all the terms used
  in stating the problem.
• Using what you are given, set up the algebra for
  the problem and solve for your answer
  algebraically
• Invent symbols for quantities you know as needed
• Dont plug in numbers until the end
• Watch your units !
• Always check the units of your answer, and carry
  the units along with your formula during the
  calculation.
• Understand the limits !
• Many equations we use are special cases of more
  general laws. Understanding how they are derived
  will help you recognize their limitations (for
  example, constant acceleration).

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Recap of todays lecture

• Scope of this course
• Measurement and Units (Chapter 1)
• Systems of units (Text 1-2)
• Converting between systems of units (Text 1-3)
• Dimensional Analysis (Text 1-4)
• 1-D Kinematics (Chapter 2)
• Average instantaneous velocity and
  acceleration (Text 2-1, 2-2)
• Motion with constant acceleration (Text 2-3)
• Example car problem
• Dont forget to register your i-clicker.