**Unformatted text preview: **Why Study Physics?
Physics 317K
G
General
l Physics
Ph i I
TTH 9:30-11 AM (#56695)
TTH 2-3:30
2 3 30 PM (#56700)
•
•
utexas edu • Physics attempts to discover the physical laws that govern the
natural world. These laws apply equally to living and nonliving
systems and form the basis of all other sciences
sciences.
• In future courses you will encounter materials that depend on
understanding basic physics.
• Modern technologies such as computers, cell phones, lasers,
and MRI have been made possible by advances in physics, and
this will continue to be true for future innovations.
innovations
• Gaining knowledge in basic physics has become an integral
part of a complete
p
p
education.
• A training in physics prepares one to solve problems regardless
of the subject matter. Outline of Course Contents
Textbook • Recommended: Richard Wolfson, Essential
U i
University
it Ph
Physics,
i
3rdd Edition,
Editi
V
Volume
l
1
1.
• You may also use other standard introductory physics
books. Check out the large collection in the PMA library.
• Free textbook from Rice University’s OpenStax College:
. • Mechanics
• Oscillations and Waves
– 1D and 2D Motion
– Simple
p Harmonic
– Newton’s Laws
Oscillations
– Energy Conservation
– Wave Motion
– Momentum Conservation
– Sound
– Rotational Motion and
angular momentum
• Heat and Thermodynamics
– Thermal Physics
• Fluid Mechanics
– Energy Transfer
− Statics of Fluids
– Laws of Thermodynamics
− Dynamics of Fluids Instructor and TA
• Instructor
– Zhen Yao, [email protected], 471-1058, RLM 13.208
– Office Hours:
• Right after each class outside PAI 2.48
• Tuesday and Thursday11:30 am – 12:30 pm in RLM
13 208
13.208
• Other times by appointment
• Teaching Assistant(s)
– TBA
– Discussion Sessions: TBA
– Office Hours: TBA Administrative Issues
• Course Pre- and Co-Requisites: Credit with a grade of at
least C
C- in Mathematics 408C or 408R; or credit with a
grade of at least C- in 408K or 408N and registration in 408L
or 408S; credit with a grade of at least C- or registration in
Physics 117M.
• Any questions – see Ms.
Ms Kelly McCoy,
McCoy Undergraduate
Office, RLM 5.214, 471-8856 How to Do Well in Class
• Basic Learning Steps
– Read about the topic (Textbook): Before coming to class you
are expected to have read the relevant materials from the
t tb k for
textbook
f that
th t day.
d
Ideally
Id ll you should
h ld come tto class
l
with
ith
many questions.
– Untangle
g it ((Lectures):
) The lectures will not simply
p y regurgitate
g g
what you have read, rather they will focus on resolving the
misconceptions and difficulties that you may have, with the
help of demonstrations and interactive quiz questions and
examples.
– Challenge yourself (Homework): Try yourself before getting
h l
help.
– Close the loop (Discussion sessions and office hours)
• Your participation is required both prior to and during each lecture
• Make sure to understand not memorize the materials
• It is essential to keep up! Grading
• Homework 25% • Midterm Exams 40% • Final Exam 35% • Semester grades will be determined by a class curve at the
end of the semester and no prescribed cutoff values should
be assumed. Typical Grade Scale
•
•
•
•
•
•
•
•
•
•
•
• A
A
AB+
B
BC+
C
CD+
D
DD
F >90
>85
>80
>75
>70
>65
>60
>55
>50
>45
>40
40
<40 Midterm Exams and Final Exam
• Three evening midterm exams from 8 to 10 pm on Tuesdays
February 14, March 21, and April 18.
• The lowest midterm grade will be dropped.
• No makeup midterm exam will be given. If you miss a midterm
exam, the
th missing
i i one will
ill b
be th
the one th
thatt will
ill b
be d
dropped.
d
• The final exam will be held on Tuesday May 16, 9 am to noon
for the TTH 9:30-11 section
section, or on Friday May 12
12, 9 am to noon
for the TTH 2-3:30 section, as scheduled by the Registrar’s
Office; no early final exam will be given
• The final exam is comprehensive and mandatory
• All exams are closed book.
• A formula sheet will be provided to you during each exam.
• Calculators may be used for numerical calculations only. Quest Homework Server
• Download homework and submit answers at
• Cost recovery charge of $30 per course ($60 for two or
more courses) to use Quest
• No late homework will be accepted
accepted.
• Lowest 2 homework grades will be dropped.
• Do the homework yourself
yourself. Copying answers deprives you
of the value of homework problems and will hurt your exam
grades.
• Start working on your homework as soon as possible and as
soon as you have obtained an answer to a problem, submit
it — do
don’t wait
a u
until you have
a e so
solved
ed a
all the
eo
other
e p
problems.
ob e s. Units, Standards, and the SI System
• W
We will
ill be
b primarily
i
il working
ki iin th
the SI system,
t
where
h
th
the b
basic
i mechanical
h i l
units are kilograms, meters, and seconds.
• The meter is the length
g of the p
path traveled by
y
light in vacuum during a time interval of
1/299,792,458 of a second.
• The second is the duration of 9,192,631,770
periods of the radiation corresponding to the
transition between two hyperfine levels of the
ground state of the cesium-133 atom.
• The kilogram is defined by the mass of a
platinum-iridium cylinder kept at the
International Bureau of Weights and Measures
at Sèvres,
Sèvres France.
France
• Other systems include cgs unit systems and
US customary unit systems.
PT.3.2448 Scientific Notation and SI Prefixes
• The vast range of quantities that
occur in physics are best expressed
with ordinary-sized numbers
multiplied by powers of 10:
– 31416.5
31416 5 = 3.1416510
3 14165 104
– 0.002718 = 2.71810–3 • Standard SI prefixes describe
powers of 10. Every three powers of
10 gets a different prefix. Clicker Question
How many femtoseconds are there in one minute? 1.
2.
3.
4.
5
5. 3.6 × 1018
6.0 × 1016
6.0 × 1015
1.7 × 1013
1 7 × 1014
1.7 Clicker 1-14 Unit Conversion
• Units matter! Measures of physical quantities must always
have the correct units.
• Convert units by multiplying or dividing so that the units you
don’t want cancel, leaving only the units you do want.
– Example: On an interstate highway, a car is traveling at a
speed of 38.0 m/s. Is the driver exceeding the speed limit
of 75.0
75 0 mi/h? 38 m s 38 1609 mi 85 mi h
1 3600 h Clicker Question Clicker Question Modern electroplaters can cover a surface area of 60 m2
with one troy
y ounce of gold
g
((volume = 1.611 cm3 )).
What is the thickness of the electroplated gold? 1.
2
2.
3.
4. A cement truck can pour 20 cubic yards of cement per
hour Express this in ft3 /min.
hour.
/min
1.
1
2.
3
3.
4. 2.68 x 10-8 m
1 34 x 10-9 m
1.34
1.67 x 10-6 m
3.33 x 10-7 m Clicker 1-17 1/3 ft3/min
1.0 ft3/min
3 ft3/min
9 ft3/min Clicker 1-18 In this lecture you’ll learn Chapter 2 Lecture • The fundamental quantities that
describe motion
– Position
– Velocity
– Acceleration
• The difference between average
and instantaneous quantities
• How to solve problems involving
constant acceleration in one
d e so
dimension
– Including the constant
acceleration of gravity near
E th’ surface
Earth’s
f Motion in a Straight Line Slide 2-1 Position and Displacement Slide 2-2 Average Velocity
• Velocity is the rate of change of position (SI unit: m/s)
– Average velocity over a time interval ∆t is defined as the
displacement divided by the time:
x
v
t
– Average speed is distance divided by time • IIn one dimension,
di
i
position
iti can b
be
described by a positive or negative
number on a number line, also
called a coordinate system.
– Position zero, the origin of the
coordinate system,
system is arbitrary
and you’re free to choose it
wherever it is convenient.
• Displacement, denoted by ∆x, is
change in position:
∆x = x2–xx1
where x1 and x2 are the initial
and final positions, respectively. Slide 2-3 Slide 2-4 Instantaneous Velocity Clicker Question • Instantaneous velocity is
the limit of the average
velocity as the time interval
becomes arbitrarily short:
− In calculus, this limiting
procedure defines the
derivative dx/dt Michael rides his bike to a store 6 miles away. He rides at a
speed
p
of 12 mph
p for the first half of the trip
p and then at 6 mph
p
for the remainder. What is his average speed for the entire trip?
1.
2.
3.
4.
5
5. x dx t0 t
dt v lim – Instantaneous speed is the
magnitude of instantaneous
velocity. 7 mph
8 mph
9 mph
10 mph
11 mph
h Slide 2-5 Clicker Question Clicker Question The figure
Th
fi
shows
h
the
th position
iti off a squirrel
i l vs. titime as it runs iin a
straight line along a telephone wire. During what time interval
does the squirrel
q
have the g
greatest speed?
p 1.
2.
3
3.
4.
5
5. Slide 2-6 Which people have the same average velocity during the
entire time p
period shown? 1.
2.
3
3.
4.
5. From A to B
From B to C only
F
From
B to
t D
From C to D only
From D to E Slide 2-7 none
Amy and Brad
Amy and Cate
Brad and Cate
all three are the same Slide 2-8 Clicker Question Clicker Question The figure shows position-versus-time graphs for four
objects. Which starts slowly and then speeds up? Suppose the position for a moving object is given by:
x(t) = 3t2+2t+5, where x is measured in meters and t is
measured in seconds
seconds. Find the velocity at t = 2 ss. 1.
2.
3.
4. A. B. C. 6 m/s
10 m/s
13 m/s
14 m/s D. Clicker 2-9 Acceleration Example • Acceleration is the rate of change
g
2
of velocity (SI unit: m/s ).
– Average acceleration over a
time interval ∆t is defined as the
change in velocity divided by the
v
time:
a
t
– Instantaneous acceleration is
the limit of the average
acceleration as the time interval
becomes arbitrarily short:
a lim t 0 Clicker 2-10 A 50-gram superball traveling at 25 m/s is bounced off a
brick wall and rebounds at 22 m/s. A high-speed
camera records this event. If the ball is in contact with
the wall for 3.5 ms, what is the magnitude of the
average acceleration of the ball during this time
interval?
1.
1
2.
3
3.
4. v dv t
dt –A
Acceleration
l ti corresponds
d tto th
the
slope of the velocity vs. time
graph. Slide 2-11 13,428
13
428 m/s
/ 2
6,715 m/s2
857 m/s2
20 m/s2 Slide 2-12 Position, Velocity, and Acceleration Clicker Question • Individual values of position, velocity, and acceleration aren’t
aren t
related.
– Velocity depends on the rate of change of position.
– Acceleration depends on the rate of change of velocity.
– An object can be at position x = 0 and still be moving.
– An
A object
bj t can h
have zero velocity
l it and
d still
till b
be accelerating.
l ti
Ball thrown
straight
g up:
p At
the peak of its
trajectory,
the ball has zero
velocity,
y, but
it’s still
accelerating. 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.
Clicker 2-14 Slide 2-13 Constant Acceleration Example • With constant acceleration
• When acceleration is
constant, then displacement,
– Velocity is a linear
velocity, acceleration, and
function of time
ti
time
are related
l t db
by
– Displacement is a
quadratic function of time
v v at
0 x 1
2 v0 v t x v0 t 12 at 2 An aircraft has a lift-off speed of 120 km/hr. What
minimum constant acceleration does this require if
the aircraft is to be airborne after a take-off run of 240
m?
1.
2.
3.
4. v 2 v02 2 a x
where
h
x0 and
d v0 are initial
i iti l
values at time t = 0, x and v
are the values at an arbitraryy
time t, and ∆x = x–x0 is the
displacement.
Slide 2-15 2.32
3 m/s
/s2
3.63 m/s2
4.64 m/s2
5.55 m/s2 Slide 2-16 Example Clicker Question
A car traveling at an initial speed v0 brakes and comes to a
complete stop in a distance d. With the same braking force,
what distance does the car travel before coming to rest if its
initial speed is 2v0? An automobile driver puts on the brakes and
decelerates from 28 m/s to zero in 12 s. What
distance does the car travel? 1.
2
2.
3.
4
4. A.
B.
C.
D.
E
E. 168 m
196 m
336 m
392 m 2d
4d
d/2
d/4
d Clicker 2-18 Slide 2-17 The Acceleration of Gravity Clicker Question • The acceleration of g
gravity
y at any
y
point is exactly the same for all
objects, regardless of mass.
• Near
N
E
Earth’s
th’ surface,
f
the
th value
l off the
th
acceleration is essentially constant at
g = 9.8 m/s2.
• Therefore the equations for constant
acceleration apply:
– In
I a coordinate
di t system
t
with
ith y axis
i
upward, they read In the absence of air friction, an object dropped near
the surface of the Earth experiences a constant
acceleration
l ti off about
b t 9.8
9 8 m/s
/ 2. This
Thi means that
th t the
th
1 the rate at which the position of the object changes as
1.
a function of time equals 9.8 m/s2.
2. object falls 9.8 meters during each second.
3 speed
3.
d off the
th object
bj t increases
i
9
9.8
8 m/s
/ d
during
i each
h
second.
4. object
j
falls 9.8 meters during
g the first second only.
y
5. speed of the object as it falls is 9.8 m/s. v v0 gt
y 1
2 v0 v t y v0 t 12 gt 2
v 2 v02 2 g y Stroboscopic photo
of a falling ball Slide 2-19 Clicker 2-20 Clicker Question Clicker Question On p
planet X,, a cannon ball is fired straight
g upward.
p
The p
position
and velocity of the ball at many times are listed below. Note that
y
we have chosen up as the positive direction.
Time(s) Height(m) A ball is thrown straight up
up. At the top of its trajectory
trajectory, its Velocity(m/s) 0 0 20 1 17 5
17.5 15 2 30 10 3 37.5 5 4 40 0 5 37.5 -5 6 30 -10
10 7 17.5 -15 8 0 -20 What is the acceleration due to
gravity on Planet X?
A.
B.
C.
D.
E. -5 m/s2
-10 m/s2
-15
15 m/s2
-20 m/s2
None of these. A. velocity
A
l it iis zero,
B. velocity is non-zero,
C. velocity is zero,
D. velocity is non-zero, acceleration
l ti is
i zero.
acceleration is non-zero.
acceleration is non-zero.
acceleration is zero. Clicker 2-21 Clicker Question Clicker 2-22 Clicker Question Find the maximum height h of a ball thrown vertically
upward with an initial velocity v0 = 30 m/s (assume g = 10
m/s2) A ball is thrown straight upward with an initial velocity vo.
Assume no air resistance.
If the initial velocity vo is doubled, the time to reach the
apex of the trajectory:
A) Doubles
B) Increases by a factor of 4 A. 45 m
B 60 m
B.
C. 90 m If the initial velocity vo is doubled, the maximum height of
the ball:
A) Doubles
B) Increases by a factor of 4
Clicker 2-23 Clicker 2-24 Clicker Question Summary Standing on a roof, you simultaneously throw one ball straight
up and another one straight down with the same initial speed.
Neglecting air resistance, which ball hits the ground with
greater speed?
A. The ball thrown straight down
A
B. The ball thrown straight up
C. Both balls have the same speed. • Position, velocity, and acceleration are the fundamental quantities
describing motion.
– Velocity is the rate of change of position.
– Acceleration
A
l ti iis th
the rate
t off change
h
off velocity.
l it • When acceleration is constant, simple
equations relate position, velocity,
acceleration and time
acceleration,
time.
– An important case is the acceleration
due to gravity near Earth’s surface.
– The magnitude of the gravitational
acceleration is g = 9.8 m/s2.
Clicker 2-25 v v 0 at
x 1
2 v0 v t x v 0 t 12 at 2
v 2 v 02 2 a x
Slide 2-26 In this lecture you’ll learn Chapter 3 Lecture Motion in Two and Three
Di
Dimensions
i Slide 3-1 Vectors • To describe position
position, velocity
velocity, and
acceleration in three-dimensional
space using the language of
vectors
• To resolve a vector into its
components
• To manipulate vectors algebraically
• To transform velocities to different
reference frames
• To solve problems involving
constant
t t acceleration
l ti in
i two
t
dimensions
– Including projectile motion due
to the constant acceleration of
gravity near Earth’s surface Slide 3-2 Adding Vectors • A vector is a quantity that has both magnitude and direction.
direction
– In two dimensions it takes two numbers to specify a
vector.
– In three dimensions it takes three numbers.
– A vector can be represented by an arrow whose length
corresponds to the vector’s magnitude
magnitude. • To add vectors graphically, place the tail off the second
vector at the head of the first.
– Their sum is then the vector from the tail of the first
vector to the head of the second.
– Here is the sum of and . • Position is a vector quantity.
– An
A object’s
bj
position
i i iis
specified by giving its distance
g and its direction
from an origin
relative to an axis.
– Here describes a point 2.0
m from the origin at a 30˚
30
angle to the axis.
Slide 3-3 Slide 3-4 Vector Arithmetic Clicker Question • Vector addition is comm
commutative
tati e and associati
associative
e
• To subtract vectors, add the negative of the second vector
to the first: Which figure shows • To multiply a vector by a scalar, multiply the vector’s
magnitude
i d b
by the
h scalar.
l
– For a positive scalar the direction is unchanged.
– For a negative scalar the direction reverses
reverses. Clicker 3-6 Slide 3-5 Clicker Question Clicker Question Which figure shows
Let the magnitudes of two displacement vectors be 20 m and
40 m,
m respectively
respectively. If the two vectors are added
added, what is the
only possible magnitude of the resultant vector out of the
following choices?
A.
B
B.
C.
D
D.
E. Clicker 3-7 0m
18 m
37 m
64 m
100 m Clicker 3-8 Vector Components Adding Vectors by Components • Any
y vector in 2D can be written as
the sum of two perpendicular vectors,
which are called its components • To add vectors,
vectors add the individual components:
–
, then where iˆ and ˆj are unit vectors in the
x and y directions – Similarly,
Si il l Ay A sin Ay
tan A Ax2 Ay2
Ax
• Similarly, a 3D vector can be resolved
i t th
into
three perpendicular
di l components:
t Ax A cos A Ax2 Ay2 Az2
Clicker 3-9 Clicker Question Slide 3-10 Clicker Question What are the x- and y-components Cx and Cy of vector
What is the correct expression for Ay, the y-component of the
vector A?
y 1)
2)
3)
4)
5) 1)
2)
3)
4)
5) Cx= –3 cm, Cy = 1 cm
Cx= –4 cm, Cy = 2 cm
Cx= –2 cm, Cy = 1 cm
Cx= –3
3 cm
cm, Cy = –1
1 cm
Cx= 1 cm, Cy = –1 cm
Clicker 3-11 A cos
A sin
-A cos
-A sin
N
None
off these
th x A Clicker 3-12 Clicker Question Example The figure shows two vectors lying in the xy-plane.
Determine the signs of the x- and y-components of A, B,
and A+B.
1. Ax and Bx are both positive,
the rest negative. 2
2. Ax and Bx are both
negative, the rest positive. 3. Ay and Bx are both p
positive,
the rest negative. An ant on a picnic table travels 30 cm eastward
eastward, then
25 cm northward and finally 15 cm westward. What is
the magnitude of its net displacement?
1.
2.
3.
4. 29 cm
70 cm
57 cm
52 cm Clicker 3-13 Example Slide 3-14 Displacement and Velocity Vectors
• Position of a particle: An ant on a picnic table travels 30 cm eastward, then
25 cm northward and finallyy 15 cm westward. What is
its directional displacement with respect to its original
position?
1.
2
2.
3.
4
4. • Displacement vector:
• Velocity is the rate of change of position
− Average
e age velocity
e oc ty
− Instantaneous velocity 59° N of E
29° N of E
29° N of W
77° N of E
77 vx dx
dy
dz
vy vz dt
dt
dt − Instantaneous velocity is always tangent to the path of
the particle at every point
Slide 3-15 Slide 3-16 Velocity and Acceleration Vectors Clicker Question • Acceleration is the rate of change
g of velocity
y
An airplane makes a gradual 90 turn while flying at a
constant speed of 200 m/s. The process takes 20 s
to complete. For this turn, the magnitude of the
average acceleration of the plane is: – Average acceleration:
– Instantaneous accel.:
• How the velocity
y evolves depends
p
on the magnitude
g
of the
acceleration as well as its direction:
In general:
g
both speed and direction change 1.
2.
3.
4.
5. 40 m/s2
14 m/s2
0 m/s2
10 m/s2
20 m/s2 Slide 3-17 Relative Velocity
• An object
j
moves with velocity
y relative
to one frame of reference, S’.
• S’ moves at relative to a second
reference
f
f
frame,
S.
S
• From the diagram, Slide 3-18 C...

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