Physics 111: Lecture 1 Mechanics for Physicists and Engineers Agenda for Today

1
Physics 111 Lecture 1Mechanics for Physicists
and EngineersAgenda for Today

• Advice
• 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

2
Course Info Advice

• See info on the World Wide Web (heavily used in
  Physics 111)
• Go to http//www.physics.uiuc.edu and follow
  courses link to the Physics 111 homepage
• Course has several components
• Lecture (me talking, demos and Active learning)
• Discussion sections (group problem solving)
• Homework sets, Web based
• Labs (group exploration of physical phenomena)
• If you miss a lab or discussion you should always
  try to make it up as soon as possible in another
  section!!
• The first few weeks of the course should be
  review, hence the pace is fast. It is important
  for you to keep up!

3
Lecture Organization

• Three main components
• Lecturer discusses class material
• Follows lecture notes very closely
• Lecturer does as many demos as possible
• If you see it, you gotta believe it!
• Look for the symbol
• Students work in groups on conceptualActive
  Learning problems
• Usually three per lecture

4
Scope of Physics 111

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

5
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).

6
Length

• Distance Length (m)
• Radius of visible universe 1 x 1026
• To Andromeda Galaxy 2 x 1022
• To nearest star 4 x 1016
• Earth to Sun 1.5 x 1011
• Radius of Earth 6.4 x 106
• Sears Tower 4.5 x 102
• Football field 1.0 x 102
• Tall person 2 x 100
• Thickness of paper 1 x 10-4
• Wavelength of blue light 4 x 10-7
• Diameter of hydrogen atom 1 x 10-10
• Diameter of proton 1 x 10-15

7
Time

• Interval Time (s)
• Age of universe 5 x 1017
• Age of Grand Canyon 3 x 1014
• 32 years 1 x 109
• One year 3.2 x 107
• One hour 3.6 x 103
• Light travel from Earth to Moon 1.3 x 100
• One cycle of guitar A string 2 x 10-3
• One cycle of FM radio wave 6 x 10-8
• Lifetime of neutral pi meson 1 x 10-16
• Lifetime of top quark 4 x 10-25

8
Mass

• Object Mass (kg)
• Milky Way Galaxy 4 x 1041
• Sun 2 x 1030
• Earth 6 x 1024
• Boeing 747 4 x 105
• Car 1 x 103
• Student 7 x 101
• Dust particle 1 x 10-9
• Top quark 3 x 10-25
• Proton 2 x 10-27
• Electron 9 x 10-31
• Neutrino 1 x 10-38

9
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.

10
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

11
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!!

12
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 ?

P 2? (dg)2
(a)
(b)
(c)
Given d has units of length (L) and g has
units of (L / T 2).
13
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)
14
Lecture 1, Act 1 Solution

• Try the second equation

(b)
Not Right !!
(a)
(b)
(c)
15
Lecture 1, Act 1 Solution

• Try the third equation

(c)
This has the correct units!! This must be the
answer!!
(a)
(b)
(c)
16
Motion in 1 dimension

• In 1-D, we usually write position as x(t1 ).
• 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

x
some particles trajectoryin 1-D
x2
??x
x1
t
t1
t2
??t
17
1-D kinematics

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

x
trajectory
x2
??x
Vav slope of line connecting x1 and x2.
x1
t
t1
t2
??t
18
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
19
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
20
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
21
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
22
1-D Motion with constant acceleration

• High-school calculus
• Also recall that
• Since a is constant, we can integrate this using
  the above rule to find
• Similarly, since we can
  integrate again to get

23
Recap
Plane w/ lights

• So for constant acceleration we find

x
t
v
t
a
t
24
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
25
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
26
Derivation

• Plugging in for t

27
Average Velocity

• Remember that

v
v
vav
v0
t
t
28
Recap
Washers

• For constant acceleration

• From which we know

29
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

30
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
v 0
x xf , t tf
31
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

32
Problem 1...

• To find stopping distance we use

• In this case v vf 0, x0 0 and x xf

33
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

34
Tips

• Read !
• 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.
• Watch your units !
• Always check the units of your answer, and carry
  the units along with your numbers 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).

35
Recap of todays lecture

• Scope of this course
• Measurement and Units (Chapter 1)
• Systems of units (Text 1-1)
• Converting between systems of units (Text 1-2)
• Dimensional Analysis (Text 1-3)
• 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 (Ex. 2-7)
• Look at Text problems Chapter 2 6, 12, 56, 119