PHYSICS 113 SYLLABUS
Physics 113-A Fall 2010
Prof. Jed Macosko
Office: Olin 215, Lab: Olin 213
Phone: 758-4981
e-mail: macoskjc@wfu.edu
OFFICE HOURS
TF 2:30-3:30 pm R 10-11 am, 215 Olin
Feel free to drop by any time and I’ll try to accommodate you.
Physics 113 is the first course in a two-semester sequence in calculus-based general physics.
It does require the use of calculus and simple vector calculations.
SCHEDULE
- Lectures: Mon, Wed, Fri 11:00 – 11:50 am
-Each student must also enroll for one laboratory session.
- Lab sessions begin the week of Monday, August 30. (see which day and time your
particular lab session will be)
TEXT AND MATERIALS
The text is the eighth edition of Physics for Scientists and Engineers by Serway & Jewett.
You’ll need an i-Clicker ($36) for class and the lab manual (~ $10) for lab from the bookstore.
EXAMS AND GRADING
There will be one final exam and three 50-minute, in-class midterm exams given at the dates
listed below. Homework problems will be assigned for each chapter (due two lecture days
later) and they will be also be graded.
Homework:
20%
93 1/3  G  100, A;
Laboratory:
13%
90  G < 93 1/3, A;
86 2/3  G < 90, B+;
Worst test score:
10%
83 1/3  G < 86 2/3, B;
Intermediate test score:
14%
80  G < 83 1/3, B;
Best test score:
19%
76 2/3  G < 80, C+;
Final exam:
20%
73 1/3  G < 76 2/3, C;
Homework notebook:
1%
70  G < 73 1/3, C;
66 2/3  G < 70, D+;
Class participation (i-clickers):
3%
63 1/3  G < 66 2/3, D;
First class: Aug. 25, 2010
60  G < 63 1/3, D;
Last day to drop class: Sept 29, 2010
G < 60, F.
Exam 1:
Exam 2:
Exam 3:
Final:
Monday, Sept. 20, 2010
Wednesday, Oct. 20, 2010
Monday, Nov. 22, 2010
Tuesday, Dec. 7, 2009, 2:00 pm
HOMEWORK AND PROBLEM SOLVING
Homework and problem solving is a very important part of learning in a course in physics.
Approximately 5-10 questions or problems per chapter will be assigned as homework. We
will use WebAssign. Homework is due two lectures after it has been assigned. No late
homework is accepted. Some problems may also re-appear on the exams and the final.
POSTINGS
Homework, exam solutions and other material relating to the course will be posted on the
web site for the class:
http://www.wfu.edu/~macoskjc/Courses/113Fall10.htm
This class does not use CourseInfo or Blackboard.
WebAssign http://www.webassign.net/ will be implemented for standard homework
assignments. You have nine attempts to get the answers right (Demo follows).
ATTENDANCE
It is expected that students attend all scheduled classes and laboratory sessions. Attendance
at the three exams and the final is required - absence will result in a zero grade unless an
official excuse is presented. Excuses should be reported to me in advance or as soon as
possible.
Tentative outline of class (date numbers are wrong!)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Aug. 24
Introduction
Chapter 1
Aug. 25
Aug. 26
Chapter 2
Motion in 1D
Aug. 27
Aug. 28
Aug. 29
Ch. 2: 1-D motion
Last day of “free”
Drop/Add
Aug. 30
Aug. 31
Chapter 3
Vectors
Sept. 1
Sept. 2
Chapter 3
Vectors
Sept. 3
Sept. 4
Sept. 5
Chapter 4
Motion in 2D
Sept. 6
Sept. 7
Chapter 4
Motion in 2D
Last day to add courses
Sept. 8
Sept. 9
Chapter 5
Force & Motion I
Sept. 10
Sept. 11
Sept. 12
Chapter 5
Force & Motion I
Sept. 13
Sept. 14
Chapter 6
Force & Motion II
Sept. 15
Sept. 16
Catch-up & Review
Sept. 17
Sept. 18
Sept. 19
Midterm 1
Chapters 1-6
Sept. 20
Sept. 21
Chapter 7
Energy Transfer
Sept. 22
Sept. 23
Chapter 7
Energy Transfer
Sept. 24
Sept. 25
Sept. 26
Chapter 8
Potential energy
Sept. 27
Sept. 28
Chapter 8
Potential energy
Last day to drop class
Sept. 29
Sept. 30
Chapter 9
Linear Momentum
and Collisions
Tentative outline of class (date numbers are wrong!)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Oct. 1
Oct. 2
Oct. 3
Chapter 9
Linear Momentum
and Collisions
Oct. 4
Oct. 5
Chapter 10
Rotation
Oct. 6
Oct. 7
Chapter 10
Rotation
Oct. 8
Oct. 9
Oct. 10
Chapter 11
Angular Momentum
Oct. 11
Oct. 12
Chapter 11
Angular Momentum
Oct. 13
Oct. 14
Fall Break
Oct. 15
Oct. 16
Oct. 17
Catch-up and
review
Oct. 18
Oct. 19
Midterm 2
Chapters 7-11
Oct. 20
Oct. 21
Chapter 12
Static Equilibrium
Oct. 22
Oct. 23
Oct. 24
Chapter 13
Universal
Gravitation
Oct. 25
Oct. 26
Chapter 13
Universal Gravitation
Oct. 27
Oct. 28
Chapter 14
Fluids
Oct. 29
Oct. 30
Oct. 31
Chapter 14
Fluids
Tentative outline of class (date numbers are wrong!)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Nov. 1
Nov. 2
Chapter 15
Oscillations
Nov. 3
Nov. 4
Chapter 15
Oscillations
Nov. 5
Nov. 6
Nov. 7
Chapter 16
Waves I
Nov. 8
Nov. 9
Chapter 16
Waves I
Nov. 10
Nov. 11
Chapter 17
Waves II
Nov. 12
Nov. 13
Nov. 14
Chapter 18
Waves III
Nov. 15
Nov. 16
Catch-up & Review
Nov. 17
Nov. 18
Midterm 3
Chapters 12-18
Nov. 19
Nov. 20
Nov. 21
Chapter 19
Temperature
Nov. 22
Nov. 23
Thanksgiving break
Nov. 24
Thanksgiv
ing break
Nov. 25
Thanksgiving break
Nov. 26
Nov. 27
Nov. 28
Chapter 19
Temperature
Nov. 29
Nov. 30
Chapter 20
Thermodynamics
Tentative outline of class (date numbers are wrong!)
Monday
Dec. 5
Dec. 12
Winter break
Tuesday
Dec. 6
Final
2 PM
(section B)
Wednesday
Dec. 7
Thursday
Friday
Saturday
Sunday
Dec. 1
Dec 2
Catch-Up & Review
Dec. 3
Dec. 4
Dec. 8
Dec. 9
Dec. 10
Dec. 11
Part 1: Mechanics
• Concerned with the motion of objects (larger
than atoms; slower than speed of light)
• Conservation of energy
• Conservation of momentum
• Rotation of objects
• Oscillations
• Thermodynamics
Chapter 1:
Physics and Measurement
Reading assignment (reading quiz this Friday!): Chapter 1 (and 2.1-2.6)
Homework:
Problems: Chapter 1: OQ3, 7, 10, 24, Chapter 2: OQ13
Due: Monday Aug. 30, 2009, 1 minute before midnight
Check out WebAssign: http://www.webassign.net/
Units
In mechanics the three basic quantities are:
• Length (we will use the unit meter; 1 m; Paris, 1792)
• Mass (we will use the unit kilogram; 1 kg; Paris, 1792)
• Time (we will use the unit second; 1 s)
And combinations of these units (e.g. unit of velocity: m/s)
• These are units of the SI (Système International) system
that is used throughout the world in the Sciences.
Changing units
We need to apply conversion factors (a ratio of
units that are equal to one) to get the right units
Black board example 1.1
A snail crawls along with
a speed of one inch per
minute.
What’s its speed in m/s?
See appendix for conversion factors
Significant figures
A significant figure is a reliably known figure.
Give answers in significant figures.  black board
examples.
When adding or subtracting numbers, the number of decimal places in
the result should equal the smallest number of decimal places of any
term in the sum.
When multiplying several quantities, the number of significant figures
in the final answer is the same as the significant figures in the least
accurate of the quantities being multiplied. (Same for division)
Factor
Name
Symbol
1024
yotta
Y
1021
zetta
Z
1018
exa
E
1015
peta
P
1012
tera
T
109
giga
G
106
mega
M
103
kilo
k
102
hecto
h
101
deka
da
10-1
deci
d
10-2
centi
c
10-3
milli
m
10-6
micro
µ
10-9
nano
n
10-12
pico
p
10-15
femto
f
10-18
atto
a
10-21
zepto
z
10-24
yocto
y
The 20 SI prefixes used to form
decimal multiples and submultiples
of SI units (from NIST).
Black board example 1.2
DNA has a diameter of 2x10-9 m. How
many nanometer is that?
The building blocks of matter
Atomic force microscope
image of gold surface
• All matter consists of atoms (greek: atomos = not sliceable)
• All atoms consist of a nucleus surrounded by electrons
• Nuclei consist of protons and neutrons. The sum of neutrons and protons in the nucleus
of a particular element is called the atomic mass of the element. The number of protons
is called the atomic number.
• Protons and Neutrons consist of Quarks (six different varieties)
Atomic mass of an element: average
mass of one atom in a sample of the
element.
Unit of the atomic mass: 1u = 1.66·10-27 kg
One atom of the carbon-12 isotope (12C)
has a mass of 12 u.
Density:
Density r = _______________
For example:
Density of matter depends on:
Aluminum: 2.7 g/cm3
• The atomic _____ of the individual atoms
Lead:
11.3 g/cm3
• How tightly atoms are packed
Black board example 1.3 (problem 20)
Gold, which has a mass of 19.32 g for each cubic centimeter of volume, is the most
_________ metal and can be pressed into a thin leaf or drawn out into a long fiber.
(a) If 1.000 oz of gold, with a mass of 27.63 g, is pressed into a leaf of 1.000 µm
thickness, what is the area of the leaf?
(b) (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm,
what is the length of the fiber?
Density:
Density r = mass/unit volume
For example:
Density of matter depends on:
Aluminum: 2.7 g/cm3
• The atomic mass of the individual atoms
Lead:
11.3 g/cm3
• How tightly atoms are packed
Black board example 1.3 (problem 20)
Gold, which has a mass of 19.32 g for each cubic centimeter of volume, is the most
ductile metal and can be pressed into a thin leaf or drawn out into a long fiber.
(a) If 1.000 oz of gold, with a mass of 27.63 g, is pressed into a leaf of 1.000 µm
thickness, what is the area of the leaf?
(b) (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm,
what is the length of the fiber?
Dimensional analysis
Dimensions (In this case we mean the units of a
physical quantity) can be treated as algebraic
quantities.
• Always do a dimensional analysis when solving
problems.
Black board example 1.4
Newton's law of universal gravitation is represented by the following equation.
F = GMm/r2
Here F is the gravitational force, M and m are masses, and r is a length.
Force has the SI units kg · m/s2. What are the SI units of the proportionality
constant G?
Problem solving:
• Always make sure you use the right units
(conversion may be necessary)
• Always do an order of magnitude estimation (Ask
yourself: “Does the number I’m getting make sense?).
Review:
• Length, mass, time
• SI units
• Dimensional analysis, conversion of units
• Order-of-magnitude estimates
• Significant figures
Announcements:
• Questions about WebAssign?
• My office hours: TF 2:30-3:30 pm, R 10-11 am
•Labs start next week  Bring ThinkPads to lab
•And now…for our reading quiz!!!
1. The slope of the curve in the position vs. time graph for a particle’s motion
gives
___ 1. the particle’s speed.
___ 2. the particle’s acceleration.
___ 3. the particle’s average velocity.
___ 4. the particle’s instantaneous velocity.
___ 5. not covered in the reading assignment
2. Is it possible for an object’s instantaneous velocity and instantaneous acceleration
to be of opposite sign at some instant of time?
___ 1. yes
___ 2. no
___ 3. need more information
3. Without air resistance, an object dropped from a plane flying at constant
speed in a straight line will
___ 1. quickly lag behind the plane.
___ 2. remain vertically under the plane.
___ 3. move ahead of the plane.
___ 4. not covered in the reading assignment
TUTOR & HOMEWORK SESSIONS
This year’s tutors: Xinyi Guo, Stephen Baker, and Wei Li,
Monday
Tuesday
Wednesday
Thursday
5-7
5-7
5-7
5-7
Friday
5-7
All sessions will be in room 101 (lecture room).
Tutor sessions in semesters past were very successful and received high marks from students.
All students are encouraged to take advantage of this opportunity.
Saturday
Sunday
Chapter 2: Motion in One Dimension
Reading assignment: Finish Chapter 2
Homework 2: (Due Wednesday, Sept. 2)
Chapter 2: 1, 9, 11, 37, 60
Remember: Homework 1 is due this Monday, Aug. 30.
•
•
In this chapter we will only look at motion along a line (one dimension).
Motion can be forward (positive displacement) or backwards (negative displacement)
Conceptual question 2.1
An object goes from one point in space to
another. After it arrives at its destination, its
displacement is:
1. either greater than or equal to
2. always greater than
3. always equal to
4. either smaller than or equal to
5. always smaller than
6. either smaller or larger
than the total distance it traveled.
Displacement and
total distance traveled
Displacement of a particle: Its change in position:
x  x2  x1
x final position
2
x initial position
1
Don’t confuse displacement with the total distance traveled.
Example: Baseball player hitting a home run travels a total distance of 360 ft, but his displacement is 0 ft!!
Displacement is a vector: It has both, magnitude and direction!!
Total distance traveled is a scalar: It has just a magnitude
Conceptual black board example 2.2
A person initially at point P in the illustration stays there a moment and then moves along the
axis 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 of the position vs. time graphs below correctly
represents this motion?
Velocity and speed
Average Velocity of a particle:
vavg , x
x x2  x1


t t 2  t1
x: displacement of particle
t: total time during which displacement occurred.
Average speed of a particle:
total distance
average
eed
sp

total time
Velocity is a vector: It has both, magnitude and direction!!
Speed is a scalar: It has just a magnitude
Blackboard example 2.1
The position of a car is measured every ten seconds relative
to zero.
A)
B)
C)
D)
E)
F)
30 m
52 m
38 m
0m
- 37 m
-53 m
Find the displacement, average velocity and average speed
between positions A and F.
Instantaneous velocity and instantaneous speed
x dx

t  0 t
dt
v x  lim
Instantaneous velocity is the derivative of x with respect to t, dx/dt!
Velocity is the slope of a position-time graph!
The instantaneous speed (scalar) is defined as the magnitude of its velocity (vector)
10
Blackboard example 2.2
A particle moves along the x-axis. Its
coordinate varies with time according to
the expression x = -4t + 2t2.
displacement (m)
8
6
4
x
2
0
t
-2
-4
0
0.5
1
1.5
2
2.5
3
time (s)
(a) Determine the displacement of the particle in the time intervals t=0 to t=1s and
t=1s to t=3s.
the average velocity during these two time interval.
(b) Calculate
(c) Find the instantaneous velocity of the particle at t=2.5s.
(d) Is the velocity constant or is it changing?
3.5
4
Acceleration
When the velocity of a particle (say a car) is changing, it is accelerating. (Decelerating/braking = negative
acceleration).
The average acceleration of the particle is defined as the change in velocity v divided by the
x
time interval t during which that change occurred.
aavg , x
v x v x 2  v x1


t
t 2  t1
The instantaneous acceleration equals
the derivative of the velocity with respect to time (slope of a velocity vs. time graph).
v x dv x

t 0 t
dt
a x  lim
Units: m/sec2
Because v = dx/dt, the acceleration can also be written
x
as:
dvx d  dx  d 2 x
ax 
   2
dt dt  dt  dt
1
A
2
B
parabola
3
C
Find the appropriate
acceleration graphs
Conceptual black board example 2.3
Relationship between acceleration-time, velocity-time, and displacement-time graphs.
A train car moves along a long straight track. The graph shows the position as a function of time for this train.
The graph shows that the train:
1. speeds up all the time.
2. slows down all the time.
3. speeds up part of the time and slows down part of the time.
4. moves at a constant velocity.
The graph shows position as a function of time for two trains running on parallel tracks. Which is true:
1. At time t ,both trains have the same velocity.
B speed up all the time.
2. Both trains
3. Both trains have the same velocity at some time before t .
B
4. Somewhere on the graph, both trains have the same acceleration.
Peer Instruction question:
4. can’t determine without knowing throw velocity
Chapter 2: Motion in One Dimension-continued
Reading assignment: Chapter 3
Homework 3 (due Saturday, Sept. 4, 2010):
(Chapter 3)
OQ4, 5, 9*, 29, 51
(note: problem 5 is asking for r, not x and y)
•
•
In this chapter we will only look at motion along a line (one dimension).
Motion can be forward (positive displacement) or backwards (negative displacement)
1. The slope of the curve in the position vs. time graph for a particle’s motion
gives
___ 1. the particle’s speed.
___ 2. the particle’s acceleration.
___ 3. the particle’s average velocity.
___ 4. the particle’s instantaneous velocity.
___ 5. not covered in the reading assignment
2. Is it possible for an object’s instantaneous velocity and instantaneous acceleration
to be of opposite sign at some instant of time?
___ 1. yes
___ 2. no
___ 3. need more information
Can the instantaneous velocity v of an
object at an instant of time ever be
greater in magnitude than the average
velocity, over a time interval containing
the instant? Can it ever be less?
A) v is always less than or equal to
B) v can be less than but not greater.
C) v can be greater than but not less.
D) v is always greater than or equal to
E) v can be greater than or less than
v
.
,
,
v
v
v
.
.
v
v
If an object's average velocity is nonzero over some time interval, does
this mean that its instantaneous velocity is never zero during the
interval?
A) Yes
B) No
If the velocity of a particle is nonzero, can its acceleration be zero?
a) Yes
b) No
If the velocity of a particle is zero, can its acceleration be
nonzero?
Yes
A)No
B)
Review from Friday:
•
•
•
Displacement x, velocity v, acceleration a
a = dv/dt = d2x/dt2, and v = dx/dt.
x is slope of v-graph, v is slope of a-graph.
Peer Instruction question:
4. can’t determine without knowing throw velocity
One-dimensional motion with constant acceleration
v  v0  at
1 2
x  x0  v0t  at
2
v  v0  2a( x  x0 )
2
2
x  x0  12 (v0  v)t
Derivations: Book pp. 41-42
*Velocity as function of time (2-13)
*Position as function of time (2-16)
Velocity as function of position (2-17)
Position as function of time and velocity (2-15)
General Problem-Solving Strategy
GRAPH IT! (if possible)
See the movie in your mind
Conceptualize __________________________________
Pick the example that matches
Categorize__________________________________
Do the algebra to isolate the variable
Analyze __________________________________
Make sure units and magnitude are reasonable
Finalize __________________________________
Black board example 2.7 (see book)
Spotting a police car, you brake a Porsche from a speed of 100
km/h to speed 80 km/h during a displacement of 88.0 m at a
constant acceleration.
(a) What is your acceleration?
(b) How long did it take to slow down?
Notice that acceleration and velocity often point in different
directions!!!
Black board example 2.8
A car traveling at constant speed of 45.0 m/sec passes a trooper hidden behind a
billboard. One second after the speeding car passes the billboard, the trooper sets
out from the billboard to catch it, accelerating at a constant rate of 3.00 m/s2.
(a) How long does it take her to overtake the car?
(b) How far has she traveled?
Freely falling objects
In the absence of air resistance, all objects fall towards the earth with the same constant acceleration (a
= -g = -9.8 m/s2), due to gravity
Black board example 2.9
A stone thrown from the top of a building is given an initial
velocity of 20.0 m/s straight upward. The building is 50 m
high. Using t = 0 as the time the stone leaves the throwers
A A, determine:
hand at position
(a)
(b)
(c)
The time at which the stone reaches its maximum height.
(d)
(e)
The velocity of the stone at this instant
The maximum height.
The time at which the stone returns to the position from
which it was thrown.
The velocity and and position of the stone at t = 5.00 s.
General Problem-Solving Strategy
GRAPH IT! (if possible)
See the movie in your mind
Conceptualize __________________________________
Pick the example that matches
Categorize__________________________________
Do the algebra to isolate the variable
Analyze __________________________________
Make sure units and magnitude are reasonable
Finalize __________________________________
Review (warning: “summaries” can atrophy your mind!)
• Displacement x, velocity v, acceleration a
• a = dv/dt = d2x/dt2, and v = dx/dt.
• Know x, v, a graphs. x is slope of v-graph, v is slope of a- graph.
• For constant acceleration problems (most problems, free fall):
• Equations on page 34-35 (const. Acceleration & free fall).
• Free fall
1 2
x  x0  v0t  at
2
v  v0  at
Peer Instruction question:
If I hurl a watermelon straight up at 10 m/s off the top of Wait Chapel and then hurl
another watermelon straight down at 10 m/s, which one will have a greater velocity when
it hits the ground. Assume no air resistance.
A)The first watermelon
B)The second watermelon
C)They will hit with equal velocities
D)Not enough information
Chapter 3: Vectors
Reading assignment: Chapter 3.3-3.4
Homework 4 (due Monday, Sept. 6, 2010):
Chapter 3: AE1-5, 64, 62 (AE=active exercise)
Note: a max of 10 points will be given, even when HWs have more possible points (e.g.
HW4 is has 15 possible pts)
Remember: Homework 2 is due tonight at 11:59 pm
•
•
•
•
•
WebAssign ok?
Everything all right in lab?
Questions?
In this chapter we will learn about vectors, (properties, addition, components of vectors)
Multiplication will come later
If an object's average velocity is nonzero over some time interval, does
this mean that its instantaneous velocity is never zero during the
interval?
A) Yes
B) No
Which of the following is a vector?
force
A)the height of a building
B)the volume of water in a can
C) temperature
D)the ratings of a TV show
E)the age of the Universe
F)
Is it possible to add a vector quantity to a scalar
quantity?
A)Yes
B)No
Review:
• Displacement x, velocity v, acceleration a
• a = dv/dt = d2x/dt2, and v = dx/dt.
• Know x, v, a graphs. v is slope of x-graph, a is slope of v- graph.
• For constant acceleration problems (most problems, free fall):
• Equations on page 36-7 (const. Acceleration & free fall).
• Free fall
1 2
x  x0  v0t  at
2
v  v0  at
General Problem-Solving Strategy
GRAPH IT! (if possible)
See the movie in your mind
Conceptualize __________________________________
Pick the example that matches
Categorize__________________________________
Do the algebra to isolate the variable
Analyze __________________________________
Make sure units and magnitude are reasonable
Finalize __________________________________
Freely falling objects
In the absence of air resistance, all objects fall towards the earth with the same constant acceleration (a
= -g = -9.8 m/s2), due to gravity
Vectors: Magnitude and direction
Scalars: Only Magnitude
A scalar quantity has a single value with an appropriate unit and has no direction.
Examples for each:
Vectors: Displacement, Velocity, Acceleration, Force
Scalars: Mass, Time, Distance, Speed, Density, etc.
Motion of a particle from A to B along an arbitrary path (dotted line).
Displacement is a vector
Coordinate systems
Cartesian coordinates:
Vectors:
•
•
•
•
Represented by arrows (example displacement).
Tip points away from the starting point.
Length of the arrow represents the magnitude
In text: a vector is often represented in bold face (A) or by an arrow over the
letter.
•
In text: Magnitude is written as A or

A

A
These four vectors are equal because they have the same magnitude and
point the same direction
Adding vectors:
Graphical method (triangle method):
Draw vector A.
Draw vector B starting at the tip of vector A.
The resultant vector R = A + B is drawn from the tail of A to the tip of B.
The vectors a, b, and c are related by c = b + a. Which diagram below illustrates
this relationship?
1)
2)
3)
4)
5)
I.
II.
III.
IV.
None of these
A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the
magnitude of the resultant is:
1)
zero
2)
1
3)
3
4)
5
5)
7
Adding vectors:
Graphical method (triangle method):
Draw vector A.
Draw vector B starting at the tip of vector A.
The resultant vector R = A + B is drawn from the tail of A to the tip of B.
Adding several vectors together.
Resultant vector
R=A+B+C+D
is drawn from the tail of the first vector
to the tip of the last vector.
Adding several vectors together.
Resultant vector
R=A+B+C+D
is drawn from the tail of the first vector
to the tip of the last vector.
Associative Law of vector addition
A+(B+C) = (A+B)+C
The order in which vectors are added together does not matter.
Negative of a vector.
The vectors A and –A have the same magnitude but opposite direction.
A + (-A) = 0
A
-A
The vector –2 is:
1)
2)
3)
4)
5)
longer than 2
shorter than 2
in the same direction as 2
in the direction opposite to 2
perpendicular to 2
Subtracting vectors:
A - B = A + (-B)
Blackboard example 3.1
A car travels 20.0 km due north and then 35.0 km in a direction 60° west of north as shown in the
figure.
Find the magnitude and direction of the car’s resultant displacement.
We cannot just add 20 and 35 to get resultant vector!!
Chapter 3: Vectors
Reading assignment: Chapter 3.3-3.4
Homework 4 (due Monday, Sept. 6, 2010):
Chapter 3: AE1-5, 64, 62 (AE=active exercise)
Note: a max of 10 points will be given, even when HWs have more possible points (e.g.
HW4 is has 15 possible pts)
Remember: Homework 2 is due tonight at 11:59 pm
•
•
•
•
•
WebAssign ok?
Everything all right in lab?
Questions?
In this chapter we will learn about vectors, (properties, addition, components of vectors)
Multiplication will come later
Chapter 3: Vectors
Reading Assignment: Chapter 4.1-4.3
Homework 3 (due Wednesday, Sept. 8, 2010):
Chapter 4: OQ3, 1, 7, 30, 34*
Outline
•
•
•
•
•
Vector components
Unit vectors
Polar coordinates
In this chapter we will learn about vectors, (properties, addition, components of vectors)
Multiplication will come later
A vector A lies in the xy plane. For what
orientations of A will both of its components be
negative?
a) A is between 0° and 90°
b) A is between 270° and 360°
c) A is between 90° and 180°
d) A is between 180° and 270°
For what orientations will its component
have opposite signs?
a) first quadrant
b) second quadrant
c) third quadrant
d) fourth quadrant
e) both b and d
Can the magnitude of a vector have a negative value?
Yes
a)
No
b)
Under what circumstances would a nonzero vector lying in the xy plane
ever have components that are equal in magnitude?
A) The vector is parallel to any axis.
B) The vector is oriented at 45° to any axis.
C) The vector is parallel to the +x or +y axis.
D) The vector is parallel to the -x or -y axis.
Multiplying a vector by a scalar
The product mA is a vector that has the same direction as A and magnitude mA.
The product –mA is a vector that has the opposite direction of A and magnitude
mA.
Components of a vector
The x- and y-components of a vector:
Ax  A cos 
Ay  A sin 
The magnitude of a vector:
A
Ax  Ay
2
2
The angle  between vector and x-axis:
 Ay 
  tan  
 Ax 
1
Vectors A and B lie in the xy plane. We can deduce that A = B if:
1)
2)
3)
4)
5)
A 2+A 2=B 2+B 2
x
y
x
y
A +A =B +B
x
y
x
y
A = B and A = B
x
x
y
y
A /A = B /B
y x
y x
A = A and B = B
x
y
x
y
The signs of the components A and A depend on the angle  and they can
x
y
be positive or negative.
(Examples)
Unit vectors
• A unit vector is a dimensionless vector having a magnitude 1.
• Unit vectors are used to indicate a direction.
• i, j, k represent unit vectors along the x-, y- and z- direction
• i, j, k form a right-handed coordinate system
The unit vector notation for the vector A is:
A =A i +A j
x
y
Vector addition using unit
vectors:
We want to calculate:
R=A+B
From diagram:
R = (A i + A j) + (B i + B j)
x
y
x
y
R = (A + B )i + (A + B )j
x
x
y
y
The components of R:
R =A + B
Rx = A x + B x
y
y
y
Vector addition using unit
vectors:
The magnitude of a R:
R  Rx  R y  ( Ax  Bx ) 2  ( Ay  By ) 2
2
2
The angle  between vector R and x-axis:
 Ry   Ay  By 

tan      
 Rx   Ax  Bx 
Blackboard example 3.2
Once again, dad doesn’t know where he is going. He
drives the car
-
east for a distance of 50 km,
then north for 30 km
and then in a direction 30° east of north for 25 km.
(a)
(b)
Sketch the vector diagram for this trip.
(c)
Determine magnitude and direction (angle) of the car’s total displacement R.
Determine the components of the car’s resultant displacement R for the trip. Find an expression
for R in terms of unit vectors.
• If A = (6 m)î – (8 m)j then A has
magnitude:
•
1) 10 m
•
2) 20 m
•
3) 30 m
•
4) 40 m
•
5) 50 m
Polar Coordinates
A point in a plane: Instead of x and y coordinates a point in a plane can be represented by its polar
coordinates r and .
x  r cos 
y  r sin 
y
tan  
x
r x y
2
2
Blackboard example 3.3
The Cartesian coordinates of a point in the x-y plane are
(x,y) = (-3.50, -2.50).
Find the polar coordinates of this point.
Chapter 4, part 1:
Reading assignment:
Chapter 4 (4.4-4.6)
Homework 6: (due Saturday, Sept. 11, 2011):
Chapter 4:
all AE's, 4AF's, 9, 69
In this chapter we will learn about the kinematics (displacement, velocity,
•acceleration)
of a particle in two or three dimensions.
• Uniform Circular Motion
• Superposition principle
The figure shows the velocity and acceleration of
a particle at a particular instant in three situations.
A
B
C
D
None of these three
(1) In which situation is the speed of the
particle increasing?
(2) In which situation is the speed of the
particle decreasing?
(3) In which situation is the speed not
changing?
Displacement in a plane
The displacement vector r:
  
r  r f  ri
Displacement is the straight line between the final and initial position of the
particle.
That is the vector difference between the final and initial position.

The vector r is given by
 x
 

ˆ
ˆ
ˆ
r  xi  yj  zk   y 
z
 
Average Velocity
Average velocity v:

 r
v 
t
Average velocity: Displacement of a particle, r, divided by time interval t.
Instantaneous Velocity

  dx dt 

r dr
v  lim

  dy dt 
t 0 t
dt 

dz
dt



Instantaneous velocity v : Limit of the average velocity as t approaches
zero. The direction v is always tangent to the particles path.
The instantaneous velocity equals the derivative of the position vector with
respect to time.
The magnitude of the instantaneous velocity vector is called the speed
(scalar)

v v
Average Acceleration
Average acceleration:
 
v f  vi


v
a

t f  ti
t
Average acceleration: Change in the velocity v divided by the time t during
which the change occurred.
Change can occur in direction and magnitude!
Acceleration points along change in velocity v!
Instantaneous
Acceleration

  dvx dt 

v dv
a  lim

  dv y dt 
t 0 t
dt 

dv
dt
 z

Instantaneous acceleration: limiting value of the ratio
as t goes to zero.

v
t
Instantaneous acceleration equals the derivative of the velocity vector with
respect to time.
Two- (or three)-dimensional motion with constant acceleration a
Trick 1:
The equations of motion we derived before (e.g. kinematic equations)
are still valid, but are now in vector form.
Trick 2 (Superposition principle):
Vector equations can be broken down into their x- and y- components.
Then calculated independently.
Position vector:
 

r  xi  yj
Velocity vector:



v  vx i  v y j
Two-dimensional motion with constant acceleration
Velocity as function of time

 
v f  vi  at
vxf  vxi  axt
v yf  v yi  a y t
Position as function of time:
   12
rf  ri  vi t  at
2
1 2
x f  xi  v xi t  a x t
2
1 2
y f  yi  v yi t  a y t
2
Black board example 4.1
A melon truck brakes right before
a ravine and looses a few
melons. The melons skit over
the edge with an initial
velocity of v = 10.0 m/s.
x
(a) Determine the x- and y-components of the velocity at any time and the total
velocity at any time.
(b) Calculate the velocity and the speed of the melon at t = 5.00 s.
(c) Determine the x- and y-coordinates of the particle at any time t and the position
vector r at any time t.
(d) Graph the path of a melon.
Uniform Circular Motion
 Motion in a circular path at constant speed.
• Velocity is changing, thus there is an acceleration!!
• Acceleration is perpendicular to velocity
• Centripetal acceleration is towards the center of the circle
• Magnitude of acceleration is
v2
r
is
radius
of
circle
The period is:
•
ar 
r
T
2  r
v
An airplane makes a gradual 90° turn while flying at a constant
speed of 200 m/s.
The process takes 20.0 seconds to complete. For this turn the
magnitude of the average acceleration of the plane is:
1)
zero
2)
40 m/s2
3)
20 m/s2
4)
14 m/s2
5)
10 m/s2
Relative Motion
Moving frame of reference
A boat heading due north crosses
a river with a speed of 10.0
km/h. The water in the river
has a speed of 5.0 km/h due
east.
(a) Determine the velocity of the boat.
(b) If the river is 3.0 km wide how long does it take to cross it?
A cart on a roller-coaster rolls down the
track shown below. As the cart rolls beyond
the point shown, what happens to its speed
and acceleration in the direction of motion?
1. Both decrease.
2. The speed decreases, but the acceleration
increases.
3. Both remain constant.
4. The speed increases, but acceleration
decreases.
5. Both increase.
Chapter 4, part 2:
Reading assignment: Chapter 5.1-5.4
Homework 7: (due Monday, Sept. 13, 2010):
Chapter 5: 8AE's, 4AF's, CQ13, 12, 13, 30*
In this chapter we will learn about the kinematics (displacement, velocity, acceleration) of a
•particle
in two or three dimensions.
• Projectile motion
• Relative motion
Figure 4-24 shows three situations in which identical projectiles are launched
from the ground (at the same level) at identical speeds and angles. The projectiles
do not land on the same terrain, however. Rank the situations according to the
final speeds of the projectiles just before they land, greatest first.
1) (a) > (b) > (c)
2) They all have the same final speed.
3) (c) > (b) > (a)
4) (a) > (c) > (b)
A ball thrown vertically upward reaches a maximum height
of 30. meters above the surface of Earth. At its maximum
height, what is the speed of the ball?
A) 9.8 m/s
B) 3.1 m/s
C) 24 m/s
D) 0.0 m/s
E) None of the above
An archer uses a bow to fire two similar arrows with the same string
force. One arrow is fired at an angle of 60° with the horizontal, and the
other is fired at an angle of 45° with the horizontal. Compared to the
arrow fired at 60°, the arrow fired at 45° has which of the following
properties:
1) longer horizontal range
2) shorter flight time
3) longer flight time
4) shorter horizontal range
5) Both 1 and 2
Projectile motion
Two assumptions:
1.
Free-fall acceleration g is
constant.
2.
Air resistance is negligible.
- The path of a projectile is a parabola (derivation: see book).
- Projectile leaves origin with an initial velocity of vi.
- Projectile is launched at an angle i
- Velocity vector changes in magnitude and direction.
- Acceleration in y-direction (vertical) is g.
- Acceleration in x-direction (horizontal) is 0.
Projectile motion
Superposition of motion in x-direction
and motion in y-direction
Acceleration in x-direction is 0.
Acceleration in y-direction is g.
(Constant velocity)
(Constant acceleration)
x f  xi  v xi t
1
y f  yi  v yit  a y t 2
2
vxf  vxi
v yf  v yi  gt
The horizontal motion and vertical motion are independent of each other; that is, neither motion
affects the other.
Simultaneous fall
demo
Which ball will hit the
ground first?
• Straight drop
• Straight out
• Both released at
the same time
A battleship simultaneously fires two shells at enemy ships.
If the shells follow the parabolic trajectories shown, which ship gets hit first?
1) A.
2) B.
3) Both hit at the same time.
4) Need more information.
Consider the situation depicted here. A bullet is
accurately aimed at a dangerous criminal
hanging from the gutter of a building. The target
is in range of the bullet’s minimum velocity, v
.
min
The instant the gun is fired and the bullet moves
with a speed v , the criminal lets go and drops
to the ground. oWhat happens? The bullet
1. hits the criminal regardless of the value of v (v > v
)
2. hits the criminal only if v is large enough (vo >onv min
,
o
o
min
3. misses the criminal.
where n “large enough”)
Hitting the bull’s eye. How’s that?
Demo.
Just to re-iterate:
Black board example 4.2
A rifle is aimed horizontally at a target 30 m away. The bullet hits the target 1.9 cm below the
aiming point.
(a)
(b)
What is the bullets time of flight
What is the bullets speed as it emerges from the rifle?
Black board example 4.3
A ball is tossed from an upper-story window of a building.
The ball is given an initial velocity of 8.00 m/s at an
angle of 20° below the horizontal. It strikes the ground
3.00 s later.
(a)
(b)
(c)
y

How far horizontally from the base of the building does the ball strike the ground?
Find the height from which the ball was thrown.
How long does it take the ball to reach a point 10 m below the level of launching?
x
Chapter 5: Force and Motion – I
Reading assignment: Chapter 5.5-5.8
Homework : (due Wednesday, Sept. 15, 2010)
Chapter 5: AE11, 24, 20, 33, 42, 71
•
In this chapter we will learn about the relationship between the force exerted on
an object and the acceleration of the object.
•
•
Forces
Newton’s three laws.


II. F  m  a
1. Which of these laws is not one of Newton’s laws?
___ 1. Action is reaction.
___ 2. F = ma.
___ 3. All objects fall with equal acceleration.
___ 4. Objects at rest stay at rest, etc.
2. The law of inertia
___ 1. is not covered in the reading assignment.
___ 2. expresses the tendency of bodies to maintain their state
___ 3. is Newton’s 3rd law.
3. “Impulse” is
___ 1. not covered in the reading assignment.
___ 2. another name for force.
___ 3. another name for acceleration.
of motion.
2. Astronauts on the Moon can jump so high because
___ 1. they weigh less there than they do on Earth.
___ 2. their mass is less there than it is on Earth.
___ 3. there is no atmosphere on the Moon.
3. Is the normal force on a body always equal to its
___ 1. yes
___ 2. no
___ 3. not covered in the reading assignment
weight?
Review of Chapters 2 & 4
• Displacement (position)
• Velocity
• Acceleration
Black board example 4.3
A ball is tossed from an upper-story window of a building.
The ball is given an initial velocity of 8.00 m/s at an
angle of 20° below the horizontal. It strikes the ground
3.00 s later.
y

x
(a) How far horizontally from the base of the building does the ball strike the ground?
(b) Find the height from which the ball was thrown.
(c) How long does it take the ball to reach a point 10 m below the level of launching?
Contact forces
- Involve physical contact between objects.
Field forces:
-No physical contact between objects
- Forces act through empty space
gravity
magnetic
electric
Measuring forces
- Forces are often measured by determining the elongation of a calibrated spring.
- Forces are vectors!! Remember vector addition.
- To calculate net force on an object you must use vector addition.
Newton’s first law:
In the absence of external forces (no net force):
• an object at rest remains at rest
• an object in motion continues in motion with constant velocity (constant speed,
straight line)
(assume no friction).
Or: When no force acts on an object, the acceleration of the object is zero.
Inertia: Object resists any attempt to change is velocity
Inertial frame of reference:
-A frame (system) that is not accelerating.
- Newton’s laws hold only true in non-accelerating (inertial) frames of reference!
Are the following inertial frames of reference:
- A cruising car?
- A braking car?
- The earth?
- Accelerating car?
Mass
- Mass of an object specifies how much inertia the object has.
- Unit of mass is kg.
The greater the mass of an object, the less it accelerates under the action of an
-applied
force.
-
Don’t confuse mass and weight (see later).
Newton’s second law
(Very important)
The acceleration of an object is:
-
directly proportional to the net force acting on it
and inversely proportional to its mass.


Fnet  m  a

 F
a
m
Fnet , x  m  a x Fnet , y  m  a y Fnet , z  m  a z
Unit of force:
•
The unit of force is the Newton (1N)
•
One Newton: The force required to accelerate a 1 kg mass by 1m/s2.
•
1N = 1kg·m/s2
Black board example 5.1
F = 8.0 N
2
 = 60°
2
Two forces act on a hockey puck (mass 0.3 kg) as
shown in the figure.
F = 5.0 N
1
 = - 20°
1
(a) Determine the magnitude and direction of the net force acting on the puck
(b) Determine the magnitude and the direction of the pucks acceleration.
(c) What third force (direction and magnitude) would need to be applied to the puck
so that its acceleration is zero?
Chapter 5: Force and Motion – II
Reading assignment: Chapter 5.5-5.8
Homework : (due Saturday, Sept. 18, 2010)
Chapter 6: 10AE's, 4AF's, 19, 64, 69
•
In this chapter we will learn about the relationship between the force exerted on
an object and the acceleration of the object.
•
•
Forces
Newton’s three laws.


II. F  m  a
1. Which of these laws is not one of Newton’s laws?
___ 1. Action is reaction.
___ 2. F = ma.
___ 3. All objects fall with equal acceleration.
___ 4. Objects at rest stay at rest, etc.
2. Astronauts on the Moon can jump so high because
___ 1. they weigh less there than they do on Earth.
___ 2. their mass is less there than it is on Earth.
___ 3. there is no atmosphere on the Moon.
3. Is the normal force on a body always equal to its
___ 1. yes
___ 2. no
___ 3. not covered in the reading assignment
weight?
The force of gravity and weight
•
•
•
•
Objects are attracted to the Earth.
This attractive force is the force of gravity F .
g


Fg  m  g
The magnitude of this force is called the weight of the object.
The weight of an object is, thus mg (Force required to keep mass m from falling to the ground).
The weight of an object can very with location (less weight on the moon than on earth, since g is smaller).
The mass of an object does not vary.
Don’t confuse mass and weight
Consider a person standing in an elevator
that is accelerating upward. The upward
normal force N exerted by the elevator floor on the person is
1. larger than
2. identical to
3. smaller than
the downward weight W of the person.
Newton’s third law
“For every action there is an equal and
opposite reaction.”
If two objects interact, the force F exerted by object 1 on object 2 is equal in magnitude and
opposite in direction to the force F12 exerted by object 2 on object 1:
21


F12   F21
Action and reaction forces always act on different objects.
Where is the action and reaction force?
Action-reaction pairs act on DIFFERENT
objects
n … normal force
When a body presses against a surface, the surface pushes on the body with a normal force n, that is
perpendicular to the surface.
A locomotive pulls a series of wagons. Which is the correct analysis of the situation?
1. The train moves forward because the locomotive pulls forward slightly harder on the
wagons than the wagons pull backward on the locomotive.
2. Because action always equals reaction, the locomotive cannot pull the wagons the wagons
pull backward just as hard as the locomotive pulls forward, so there is no motion.
3. The locomotive gets the wagons to move by giving them a tug during which the force on
the wagons is momentarily greater than the force exerted by the wagons on the locomotive.
4. The locomotive’s force on the wagons is as strong as the force of the wagons on the
locomotive, but the frictional force on the locomotive
is forward and large while the backward frictional force on the wagons is small.
5. The locomotive can pull the wagons forward only if it weighs more than the wagons.
Black board example 5.2
Conceptual example:
A large man and a small boy stand facing each other on frictionless ice. They put their
hands together and push against each other so that they move apart.
(a)
Who moves away with the higher speed
(a) Man
(b) Boy
(c) Same
(d) Need more info
(b)
Who moves farther while their hands are in contact?
B
A
Black board:
• Analyzing forces
• Free body diagram
• Tension in a rope = magnitude of the force that the rope exerts on object.
Analyzing forces:
Lamp hanging from a ceiling.
Net force on lamp is zero (not accelerating)
Black board example 5.3
A traffic light weighing 125 N hangs from a cable tied to two other cables fastened to a support as
shown in the figure.
Find the tension in the three cables.
Black board example 5.4 HW 38
A worker drags a crate across a factory floor by pulling on a rope tied to the crate. The worker exerts a
force of 450 N on the rope, which is inclined at 38° to the horizontal and the floor exerts a
horizontal force of 125 N that opposes the motion. Calculate the magnitude of acceleration for
the crate if
(a)
(b)
(c)
Its mass is 310 kg
Its weight is 310 N
What is it’s speed after 5 seconds?
(Always draw a diagram).
Black board example 5.5
Attwood’s machine.
Two objects of unequal mass (m and m ) are hung over a pulley.
1
2
(a) Determine the magnitude of the acceleration of the two objects and the tension in the
cord.
(b) Solve (a) for m1 = 2.00 kg and m2 = 4.00 kg.
Black board example 5.6
Two objects of mass m and m are attached by a string over a pulley as shown in the Figure. m lies on
1 . 2
2
an incline with angle
(a)
(b)
Determine the magnitude of the acceleration of the two objects and the tension in the cord.
m = 10.0 kg, m = 5.00 kg,  = 45º
1
2