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Physics 106P: Lecture 1 NotesPhysics 111: Lecture 1
Agenda for Today
Dimensional Analysis
Motion with constant acceleration
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:
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!
2
Lecture Organization
Lecturer does as many demos as possible
If you see it, you gotta believe it!
Look for the symbol
“Active Learning” problems
Scope of Physics 111
Classical:
Most everyday situations can be described in these terms.
Path of baseball
Orbit of planets
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).
Physics 111: Lecture 1, Pg *
Length:
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 104
Wavelength of blue light 4 x 107
Diameter of hydrogen atom 1 x 1010
Diameter of proton 1 x 1015
Physics 111: Lecture 1, Pg *
Time:
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 103
One cycle of FM radio wave 6 x 108
Lifetime of neutral pi meson 1 x 1016
Lifetime of top quark 4 x 1025
Physics 111: Lecture 1, Pg *
Mass:
Sun 2 x 1030
Earth 6 x 1024
Car 1 x 103
Student 7 x 101
Proton 2 x 1027
Electron 9 x 1031
Neutrino 1 x 1038
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.
9
Converting between different systems of units
Useful Conversion factors:
Physics 111: Lecture 1, Pg *
Dimensional Analysis
This is a very important tool to check your work
It’s also very easy!
Example:
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 don’t match, so answer must be wrong!!
Physics 111: Lecture 1, Pg *
Lecture 1, Act 1
Dimensional 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 ?
(a)
(b)
(c)
Given: d has units of length (L) and g has units of (L / T 2).
P = 2 (dg)2
Lecture 1, Act 1
Solution
Realize that the left hand side P has units of time (T )
Try the first equation
Lecture 1, Act 1
Lecture 1, Act 1
Try the third equation
Motion in 1 dimension
In 1D, we usually write position as x(t1 ).
Since it’s in 1D, all we need to indicate direction is + or .
Displacement in a time t = t2  t1 is
x = x(t2)  x(t1) = x2  x1
t
x
t1
t2
x
t
x1
x2
1D kinematics
Average velocity vav in the time t = t2  t1 is:
t
x
t1
t2
x
x1
x2
trajectory
t
Physics 111: Lecture 1, Pg *
1D kinematics...
t
x
t1
t2
x
x1
x2
t
so v(t2) = slope of line tangent to path at t2.
Physics 111: Lecture 1, Pg *
1D kinematics...
Average acceleration aav in the time t = t2  t1 is:
And instantaneous acceleration a is defined as:
using
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
a
v
t
t
t
More 1D 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)
t
Highschool 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:
Physics 111: Lecture 1, Pg *
Recap
x
a
v
t
t
t
Plane
Lecture 1, Act 2
Motion 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
Lecture 1, Act 2
Solution
x
a
v
t
t
t
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.
Physics 111: Lecture 1, Pg *
Derivation:
Average Velocity
Remember that
Recap:
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
x = 0, t = 0
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?
x = xf , t = tf
Problem 1...
Realize that a = ab
find 0 = v0  ab tf or
tf = v0 /ab
Problem 1...
To find stopping distance we use:
In this case v = vf = 0, x0 = 0 and x = xf
Physics 111: Lecture 1, Pg *
Problem 1...
Find that tf = 3 s and xf = 43 m
Physics 111: Lecture 1, Pg *
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).
26
Scope of this course
Converting between systems of units (Text: 12)
Dimensional Analysis (Text: 13)
1D Kinematics (Chapter 2)
Motion with constant acceleration (Text: 23)
Example car problem (Ex. 27)
Look at Text problems Chapter 2: # 6, 12, 56, 119
27
Agenda for Today
Dimensional Analysis
Motion with constant acceleration
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:
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!
2
Lecture Organization
Lecturer does as many demos as possible
If you see it, you gotta believe it!
Look for the symbol
“Active Learning” problems
Scope of Physics 111
Classical:
Most everyday situations can be described in these terms.
Path of baseball
Orbit of planets
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).
Physics 111: Lecture 1, Pg *
Length:
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 104
Wavelength of blue light 4 x 107
Diameter of hydrogen atom 1 x 1010
Diameter of proton 1 x 1015
Physics 111: Lecture 1, Pg *
Time:
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 103
One cycle of FM radio wave 6 x 108
Lifetime of neutral pi meson 1 x 1016
Lifetime of top quark 4 x 1025
Physics 111: Lecture 1, Pg *
Mass:
Sun 2 x 1030
Earth 6 x 1024
Car 1 x 103
Student 7 x 101
Proton 2 x 1027
Electron 9 x 1031
Neutrino 1 x 1038
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.
9
Converting between different systems of units
Useful Conversion factors:
Physics 111: Lecture 1, Pg *
Dimensional Analysis
This is a very important tool to check your work
It’s also very easy!
Example:
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 don’t match, so answer must be wrong!!
Physics 111: Lecture 1, Pg *
Lecture 1, Act 1
Dimensional 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 ?
(a)
(b)
(c)
Given: d has units of length (L) and g has units of (L / T 2).
P = 2 (dg)2
Lecture 1, Act 1
Solution
Realize that the left hand side P has units of time (T )
Try the first equation
Lecture 1, Act 1
Lecture 1, Act 1
Try the third equation
Motion in 1 dimension
In 1D, we usually write position as x(t1 ).
Since it’s in 1D, all we need to indicate direction is + or .
Displacement in a time t = t2  t1 is
x = x(t2)  x(t1) = x2  x1
t
x
t1
t2
x
t
x1
x2
1D kinematics
Average velocity vav in the time t = t2  t1 is:
t
x
t1
t2
x
x1
x2
trajectory
t
Physics 111: Lecture 1, Pg *
1D kinematics...
t
x
t1
t2
x
x1
x2
t
so v(t2) = slope of line tangent to path at t2.
Physics 111: Lecture 1, Pg *
1D kinematics...
Average acceleration aav in the time t = t2  t1 is:
And instantaneous acceleration a is defined as:
using
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
a
v
t
t
t
More 1D 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)
t
Highschool 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:
Physics 111: Lecture 1, Pg *
Recap
x
a
v
t
t
t
Plane
Lecture 1, Act 2
Motion 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
Lecture 1, Act 2
Solution
x
a
v
t
t
t
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.
Physics 111: Lecture 1, Pg *
Derivation:
Average Velocity
Remember that
Recap:
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
x = 0, t = 0
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?
x = xf , t = tf
Problem 1...
Realize that a = ab
find 0 = v0  ab tf or
tf = v0 /ab
Problem 1...
To find stopping distance we use:
In this case v = vf = 0, x0 = 0 and x = xf
Physics 111: Lecture 1, Pg *
Problem 1...
Find that tf = 3 s and xf = 43 m
Physics 111: Lecture 1, Pg *
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).
26
Scope of this course
Converting between systems of units (Text: 12)
Dimensional Analysis (Text: 13)
1D Kinematics (Chapter 2)
Motion with constant acceleration (Text: 23)
Example car problem (Ex. 27)
Look at Text problems Chapter 2: # 6, 12, 56, 119
27