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PHYSICS 113 SYLLABUS
Physics 113-A Fall 2010Prof. Jed Macosko
Office: Olin 215, Lab: Olin 213Phone: 758-4981
e-mail: [email protected]
OFFICE HOURSTF 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%
Laboratory: 13%
Worst test score: 10%
Intermediate test score: 14%
Best test score: 19%
Final exam: 20%
Homework notebook: 1%
Class participation (i-clickers): 3%
First class: Aug. 25, 2010Last day to drop class: Sept 29, 2010
Exam 1: Monday, Sept. 20, 2010Exam 2: Wednesday, Oct. 20, 2010Exam 3: Monday, Nov. 22, 2010Final: Tuesday, Dec. 7, 2009, 2:00 pm
93 1/3 G 100, A;
90 G < 93 1/3, A;
86 2/3 G < 90, B+;
83 1/3 G < 86 2/3, B;
80 G < 83 1/3, B;
76 2/3 G < 80, C+;
73 1/3 G < 76 2/3, C;
70 G < 73 1/3, C;
66 2/3 G < 70, D+;
63 1/3 G < 66 2/3, D;
60 G < 63 1/3, D;
G < 60, F.
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.
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
Thanksgiving
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 Tuesday Wednesday Thursday Friday Saturday Sunday
Dec. 1 Dec 2
Catch-Up & Review
Dec. 3 Dec. 4
Dec. 5 Dec. 6
Final
2 PM (section B)
Dec. 7 Dec. 8 Dec. 9 Dec. 10 Dec. 11
Dec. 12
Winter break
Tentative outline of class (date numbers are wrong!)
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
A snail crawls along with a speed of one inch per minute.
What’s its speed in m/s?
See appendix for conversion factors
Black board example 1.1
A significant figure is a reliably known figure. Give answers in significant figures. black board examples.
Significant figures
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).
DNA has a diameter of 2x10-9 m. How many nanometer is that?
Black board example 1.2
The building blocks of matter
• 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 force microscope
image of gold surface
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 = _______________
For example:
Aluminum: 2.7 g/cm3
Lead: 11.3 g/cm3
Density of matter depends on:
• The atomic _____ of the individual atoms
• How tightly atoms are packed
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?
Black board example 1.3 (problem 20)
Density:
Density = mass/unit volume
For example:
Aluminum: 2.7 g/cm3
Lead: 11.3 g/cm3
Density of matter depends on:
• The atomic mass of the individual atoms
• How tightly atoms are packed
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?
Black board example 1.3 (problem 20)
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.
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?
Black board example 1.4
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,
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.
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
5-7 5-7 5-7 5-7 5-7
• In this chapter we will only look at motion along a line (one dimension).
• Motion can be forward (positive displacement) or backwards (negative displacement)
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.
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.
Conceptual question 2.1
Displacement and
total distance traveled
Displacement of a particle: Its change in position:
12 xxx x
2 final position
x1
initial position
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
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?
Conceptual black board example 2.2
Velocity and speed
Average Velocity of a particle:
12
12, tt
xx
t
xv xavg
x: displacement of particle
t: total time during which displacement occurred.
Average speed of a particle:
Velocity is a vector: It has both, magnitude and direction!!
Speed is a scalar: It has just a magnitude
time total
distance total eedaverage sp
The position of a car is measured every ten seconds relative to zero.
A) 30 m
B) 52 m
C) 38 m
D) 0 m
E) - 37 m
F) -53 m
Find the displacement, average velocity and average speed between
positions A and F.
Blackboard example 2.1
Instantaneous velocity and instantaneous speed
dt
dx
t
xv
tx
0
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)
Blackboard example 2.2
A particle moves along the x-axis. Its coordinate
varies with time according to the expression x
= -4t + 2t2.
-4
-2
0
2
4
6
8
10
0 0.5 1 1.5 2 2.5 3 3.5 4
dis
pla
cem
ent
(m)
time (s)
t
x
(a) Determine the displacement of the particle in the time intervals t=0 to t=1s and t=1s to t=3s.
(b) Calculate the average velocity during these two time interval.
(c) Find the instantaneous velocity of the particle at t=2.5s.
(d) Is the velocity constant or is it changing?
Acceleration
When the velocity of a particle (say a car) is changing, it is accelerating. (Decelerating/braking = negative acceleration).
12
12, tt
vv
t
va xxx
xavg
The average acceleration of the particle is defined as the change in velocity vx
divided by the time interval t
during which that change occurred.
dt
dv
t
va xx
tx
0
lim
The instantaneous acceleration equals
the derivative of the velocity with respect to time (slope of a velocity vs. time graph).
Because vx
= dx/dt, the acceleration can also be written as:
2
2
dt
xd
dt
dx
dt
d
dt
dva x
x
Units: m/sec2
Find the appropriate
acceleration graphs
parabola
1
2
3
A
B
C
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 tB
,both trains have the same velocity.
2. Both trains speed up all the time.
3. Both trains have the same velocity at some time before tB
.
4. Somewhere on the graph, both trains have the same acceleration.
Peer Instruction question:
4. can’t determine without knowing throw velocity
• In this chapter we will only look at motion along a line (one dimension).
• Motion can be forward (positive displacement) or backwards (negative displacement)
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)
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
vv
vv
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?
A)Yes
B)No
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
atvv 0*Velocity as function of time (2-13)
)(2 02
02 xxavv Velocity as function of position (2-17)
Derivations: Book pp. 41-42
200 2
1attvxx *Position as function of time (2-16)
Position as function of time and velocity (2-15)tvvxx )( 02
10
General Problem-Solving Strategy
Conceptualize __________________________________
Categorize__________________________________
Analyze __________________________________
Finalize __________________________________
See the movie in your mindSee the movie in your mind
Pick the example that matches
See the movie in your mind
Pick the example that matches
Do the algebra to isolate the variable
See the movie in your mind
Pick the example that matches
Do the algebra to isolate the variable
Make sure units and magnitude are reasonable
GRAPH IT! (if possible)
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 tA
= 0 as the
time the stone leaves the throwers hand at position A, determine:
(a) The time at which the stone reaches its maximum height.
(b) The maximum height.
(c) The time at which the stone returns to the position from which it
was thrown.
(d) The velocity of the stone at this instant
(e) The velocity and and position of the stone at t = 5.00 s.
General Problem-Solving Strategy
Conceptualize __________________________________
Categorize__________________________________
Analyze __________________________________
Finalize __________________________________
See the movie in your mindSee the movie in your mind
Pick the example that matches
See the movie in your mind
Pick the example that matches
Do the algebra to isolate the variable
See the movie in your mind
Pick the example that matches
Do the algebra to isolate the variable
Make sure units and magnitude are reasonable
GRAPH IT! (if possible)
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
atvv 02
00 2
1attvxx
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
• In this chapter we will learn about vectors, (properties, addition, components of vectors)
• Multiplication will come later
Chapter 3: Vectors
• WebAssign ok?
• Everything all right in lab?
• Questions?
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
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?
A)force
B)the height of a building
C)the volume of water in a can
D)temperature
E)the ratings of a TV show
F)the age of the Universe
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
atvv 02
00 2
1attvxx
General Problem-Solving Strategy
Conceptualize __________________________________
Categorize__________________________________
Analyze __________________________________
Finalize __________________________________
See the movie in your mindSee the movie in your mind
Pick the example that matches
See the movie in your mind
Pick the example that matches
Do the algebra to isolate the variable
See the movie in your mind
Pick the example that matches
Do the algebra to isolate the variable
Make sure units and magnitude are reasonable
GRAPH IT! (if possible)
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:
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.
Graphical method (triangle method):
The vectors a, b, and c are related by c = b + a. Which diagram below illustrates
this relationship?
1) I.
2) II.
3) III.
4) IV.
5) 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:
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.
Graphical method (triangle method):
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
Subtracting vectors:
A - B = A + (-B)
The vector –2 is:
1) longer than 2
2) shorter than 2
3) in the same direction as 2
4) in the direction opposite to 2
5) perpendicular to 2
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!!
• In this chapter we will learn about vectors, (properties, addition, components of vectors)
• Multiplication will come later
Chapter 3: Vectors
• WebAssign ok?
• Everything all right in lab?
• Questions?
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
• In this chapter we will learn about vectors, (properties, addition, components of vectors)
• Multiplication will come later
Chapter 3: Vectors
• Vector components
• Unit vectors
• Polar coordinates
Reading Assignment: Chapter 4.1-4.3
Homework 3 (due Wednesday, Sept. 8, 2010):
Chapter 4: OQ3, 1, 7, 30, 34*
Outline
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 components 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?
a)Yes
b)No
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
sin
cos
AA
AA
y
x
22yx AAA
x
y
A
A1tan
The x- and y-components of a vector:
The magnitude of a vector:
The angle between vector and x-axis:
Vectors A and B lie in the xy plane. We can deduce that A = B if:
1) Ax2 + A
y2 = B
x2 + B
y2
2) Ax + A
y = B
x + B
y
3) Ax = B
x and A
y = B
y
4) Ay
/Ax = B
y /B
x
5) Ax = A
y and B
x = B
y
The signs of the components Ax
and Ay
depend on the angle and they can 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 = Ax
i + Ay
j
Vector addition using unit vectors:
We want to calculate: R = A + B
From diagram: R = (Ax
i + Ay
j) + (Bx
i + By
j)
R = (Ax
+ Bx
)i + (Ay
+ By
)j
The components of R:R
x = A
x + B
x
Ry
= Ay
+ By
2222 )()( yyxxyx BABARRR
xx
yy
x
y
BA
BA
R
Rtan
The magnitude of a R:
The angle between vector R and x-axis:
Vector addition using unit vectors:
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) Sketch the vector diagram for this trip.
(b) Determine the components of the car’s resultant displacement R for the trip. Find an expression for R in terms of
unit vectors.
(c) Determine magnitude and direction (angle) of the car’s total displacement R.
• 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
sin
cos
ry
rx
x
ytan 22 yxr
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.
• 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
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
The figure shows the velocity and acceleration of
a particle at a particular instant in three situations.
(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?
A B C D
None of these three
Displacement in a plane
The displacement vector r:
if rrr
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.
z
y
x
kzjyixr ˆˆˆby given is r vector The
Average Velocity
Average velocity v:
t
rv
Average velocity: Displacement of a particle, r, divided by time interval t.
Instantaneous Velocity
dtdz
dtdy
dtdx
dt
rd
t
rv
t
0lim
Instantaneous velocity : 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)
vv
v
Average Acceleration
Average acceleration:
t
v
tt
vva
if
if
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
Instantaneous acceleration: limiting value of the ratio
as t goes to zero.
Instantaneous acceleration equals the derivative of the velocity vector with respect to
time.
tv
dtdv
dtdv
dtdv
dt
vd
t
va
z
y
x
t
0lim
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.
jvivv yx
jyixr
Position vector: Velocity vector:
Two-dimensional motion with constant acceleration
tavv if
Velocity as function of time
2
2
1tatvrr iif
Position as function of time:
tavv
tavv
yyiyf
xxixf
2
2
2
12
1
tatvyy
tatvxx
yyiif
xxiif
A melon truck brakes right before a
ravine and looses a few melons.
The melons skit over the edge
with an initial velocity of vx = 10.0
m/s.
(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.
Black board example 4.1
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
• r is radius of circle The period is:
r
var
2
v
rT
2
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.
• In this chapter we will learn about the kinematics (displacement, velocity, acceleration) of a particle in two or
three dimensions.
• Projectile motion
• Relative motion
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*
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.
gtvv yiyf
2
2
1tatvyy yyiif
xixf vv
tvxx xiif
Acceleration in x-direction is 0. Acceleration in y-direction is g.
(Constant velocity) (Constant acceleration)
Projectile motion
Superposition of motion in x-direction and
motion in y-direction
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.
1. hits the criminal regardless of the value of vo
(vo
> vmin
)
2. hits the criminal only if vo
is large enough (vo
> nvmin
, where n “large enough”)
3. misses the criminal.
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, vmin
.
The instant the gun is fired and the bullet moves
with a speed vo, the criminal lets go and drops
to the ground. What happens? The bullet
Hitting the bull’s eye. How’s that?
Demo.
Just to re-iterate:
A rifle is aimed horizontally at a target 30 m away. The bullet hits the target 1.9 cm below the aiming point.
(a) What is the bullets time of flight
(b) What is the bullets speed as it emerges from the rifle?
Black board example 4.2
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) 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?
Black board example 4.3
x
y
• 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.
Chapter 5: Force and Motion – I
amF
II.
Reading assignment: Chapter 5.5-5.8
Homework : (due Wednesday, Sept. 15, 2010)
Chapter 5: AE11, 24, 20, 33, 42, 71
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 of motion.
___ 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.
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 weight?
___ 1. yes
___ 2. no
___ 3. not covered in the reading assignment
Review of Chapters 2 & 4
• Displacement (position)
• Velocity
• Acceleration
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) 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?
Black board example 4.3
x
y
Contact forces
- Involve physical contact between objects.
Field forces:
-No physical contact between objects
- Forces act through empty space
gravity
electric
magnetic
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.
amFnet
xxnet amF , yynet amF , zznet amF ,
m
Fa
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
Two forces act on a hockey puck (mass 0.3 kg) as shown
in the figure.
(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?
Black board example 5.1
F2
= 8.0 N
2
= 60°
F1
= 5.0 N
1
= - 20°
• 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.
Chapter 5: Force and Motion – II
amF
II.
Reading assignment: Chapter 5.5-5.8
Homework : (due Saturday, Sept. 18, 2010)
Chapter 6: 10AE's, 4AF's, 19, 64, 69
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 weight?
___ 1. yes
___ 2. no
___ 3. not covered in the reading assignment
The force of gravity and weight
• Objects are attracted to the Earth.
• This attractive force is the force of gravity Fg
.
• 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).
gmFg
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
If two objects interact, the force F12
exerted by object 1 on object 2 is equal in magnitude and opposite in direction
to the force F21
exerted by object 2 on object 1:
“For every action there is an equal and opposite
reaction.”
2112 FF
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.
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?
Black board example 5.2
A
B
• Analyzing forces
• Free body diagram
• Tension in a rope = magnitude of the force that the rope exerts on object.
Black board:
Analyzing forces:
Lamp hanging from a ceiling.
Net force on lamp is zero (not accelerating)
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 5.3
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) Its mass is 310 kg
(b) Its weight is 310 N
(c) 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 (m1
and m2
) are hung over a pulley.
(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 m1
and m2
are attached by a string over a pulley as shown in the Figure. m2
lies on an incline with
angle .
(a) Determine the magnitude of the acceleration of the two objects and the tension in the cord.
(b) m1
= 10.0 kg, m2
= 5.00 kg, = 45º