Chapter 1!
To do:!
Introduction to the class!
Reminder for needed math.!
Dimensional analysis!
Vectors and scalars!
Adding vectors !
Physics 203!
Professor Gunner!
[email protected]!
www.sci.ccny.cuny.edu/~gunner!
http://www.sci.ccny.cuny.edu/~gunner/Pages-203/index.html!
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Class T-Th 9:30-10:45; Fri 9:30-10:20!
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Office Hours Wed 3-4; Thurs 11-12 (MR 301)!
Grading!
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On line homework 8%!
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Lab 8%!
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3 exams 18% each!
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Final 30%!
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You cannot get a grade if you have not finished all of the
labs!
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10 pts on evey exam - an essay- what you see differently in
the world having taken this class. !
Bring print out of pre-class handout to class !
I will upload a version with answers to problems after class B
ring the calculator you will use in exams to class. !
"A scientific calculator. Not a graphing calculator. !
You cannot use your phone calculator in exams!
ExpertTA!
When students register online, they don't have to pay taxes or credit card processing fees. !
It's just a flat $27.50 for a full semester. !
That will cover assignments, tutorials, and any support requests they might have for us throughout the class. !
Please let students know they can contact us for quickest support by emailing
[email protected] - they can also use the contact us button on our website.!
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Student Registration for PHYS 20300!
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self-Registration Link: !
https://www.theexpertta.com/registration!
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Student Class Code: !
EDAFB0-LS!
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WileyPlus (for Cutnell and Johnson: $119 without the book)!
F'14 PHYS 20300 BB
"GUNNER, MARILYN"
http://edugen.wileyplus.com/edugen/class/cls411071/ "!
F'14 PHYS 20300 BB2 "GUNNER, MARILYN"
http://edugen.wileyplus.com/edugen/class/cls411073/ "!
F'14 PHYS 20300 BB3 "GUNNER, MARILYN"
http://edugen.wileyplus.com/edugen/class/cls411075/ "!
What do you need to do to win
at physics?!
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Develop an intuition for quantifying the world.!
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Learn how to put a real world situations into
mathematical language!
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I will try to use fun examples and medical and MCAT
examples. I don’t know if I can make this exciting –
but you should look at the world differently every day
given what you learn here. !
Example!
• 
You run at 10 miles/hour for an hour. How far do you
go?!
Suppose I said you went 0.1 mile or 10,000 miles
what would you think?!
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How did you solve this problem?!
You need to do simple math!
• 
• 
Algebra!
Trig!
cos θ = adj/hyp!
sin θ = opp/hyp!
tan θ= opp/adj!
!
3
!
θ
B!
!
2
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Vectors! A!
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A+B!
Graphing straight lines!
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Graphing sin or cos functions!
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Simultaneous equations!
If you are having trouble
with math!
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Find a book or on line source and practice!
• 
Do more problems for each chapter. Go carefully
over chapter 1. !
graphing straight line!
Tim
e!
X!
Red
line!
X!
Blue
line!
0!
3.2!
0!
1!
2!
4!
-8.6!
6!
8!
8.6!
m!
0.78!
0!
b!
3.2!
1.4!
Time!
x!
y=mx+b!
y=mx+b!
3.2=m(0)+b!
b=3.2!
!
9.5=m(8)+3.2!
m=0.78!
!
circle!
Circumference = 2πr!
Area= πr2!
r!
R = 10 m (1 m = 3.28 Ft)!
What is the circumference?!
2π(10m) =62.8m!
What is the area?!
πr2=314 m2!
What is the diameter?!
2*10m = 20m!
You run 10 laps around a 10 m wide circular track. !
How far did you run? !
Look at:!
http://en.wikipedia.org/wiki/Circumference!
How many ° for whole circle?!
What is a right angle?! 90°!
What is half a circle?! 180°!
360°!
1 radian!
2π radians = 6.28 radians = 360°!
1 radian = 360°/2π=360°/6.28!
1 radian = 57.3°!
Trigonometry!
θ2!
cos θ = adj/hyp!
sin θ = opp/hyp!
tan θ= opp/adj!
3!
θ1!
5!
What is the value of the hypotenuse?!
What is the cos, sin & tan of θ?!
What is the angle θ in degrees?!
!
What can we say about the hypotenuse before we do the p
roblem? What about the angle?!
Trigonometry!
θ2!
5.8!
3.0!
cos θ = adj/hyp =!
sin θ = opp/hyp =!
tan θ= opp/adj =!
θ1!
5.0!
Trigonometry!
θ2!
cos θ1 = adj/hyp=3.0/5.8=0.52!
sin θ1 = opp/hyp=5.0/5.8=0.86!
tan θ1= opp/adj=5.0/3.0= 1.67!
5.8!
3.0!
θ1!
5.0!
cos θ2 = adj/hyp=5.0/5.8=0.86!
sin θ2 = opp/hyp=3.0/5.8=0.52!
tan θ2= opp/adj=5.0/3.0= 0.60!
arc sin (0.52) =0.53 radians=30.5 degrees!
arc cos(0.86) =0.54 radians= 31.1 degrees!
arc tan (1.67) = 0.54 radian=31.0 degrees!
arc sin (0.52) =1.03 radians=58.9 degrees!
arc cos(0.86) =1.04 radians= 58.6 degrees!
arc tan (1.67) = 1.03 radian= 59.0 degrees!
Notice the connection between cos θ1 and sin θ2!
Can we tell where the sun is?!
Eratosthenes of Cyrene: 276 BCE!
!
At the Summer solstice !
"in Cyrene (Aswan) the sun casts no shadow!
"in Alexandria 800 km south the shadow is at 7.2°!
What is the diameter of the earth?!
Radius, diameter and circumference (http://www.space.com/17638-how-big-is-earth.html )!
!
The mean radius of Earth is 3,959 miles (6,371 kilometers). However, Earth is not quite a sphere. The planet's rotation caus
es it to bulge at the equator. Earth's equatorial diameter is 7,926 miles (12,756 kilometers), but from pole to pole, the diame
ter is 7,900 miles (12,720 km) — a difference of only 40 miles (64 km).!
!
The circumference of Earth at the equator is about 24,902 miles (40,075 km), but from pole-to-pole — the meridional circu
mference — Earth is only 24,860 miles (40,008 km) around. This shape, caused by the flattening at the poles, is called an o
blate spheroid.!
http://www.britannica.com/EBchecked/topic/191064/Eratosthenes-of-Cyrene!
For an explanation and a video!
Eratosthenes of Cyrene: 276 BCE!
!
At the Summer solstice !
"in Cyrene (Aswan) the sun casts no shadow!
"in Alexandria 800 km south the shadow is at 7.2°!
What is the diameter of the earth?!
http://www.britannica.com/EBchecked/topic/191064/Eratosthenes-of-Cyrene!
For an explanation and a video!
I worked out from the book!
Example 4: The height of a building!
!
Example 5: the depth of the lake!
units!
Units!
Common!
Length!
m!
yard!
mass!
kg!
(pounds are
weight not mass)!
time!
s!
Area!
m2"
ft2; mi2!
Volume!
m3"
liter; quart!
Speed!
m/s!
miles/hour!
Acceleration!
m/s3"
!
!
dimensional analysis!
60 s/min!
60 min/hour!
How many seconds in an hour?!
dimensional analysis!
65 miles/hour = ? m/s!
!
1 mile = 1609.34 m!
1 hour = 3600 s!
dimensional analysis!
60 miles/hour = ? m/s!
!
1 mile = 1609.34 m!
1 hour = 3600 s!
=29.1 m/s!
Which of these are dimensionally correct?!
!
x=vt!
!
!
x=vt + 1/2at2!
!
!
v=at!
!
!
v3=2ax2!
x=m (length)!
v=m/s (velocity)!
t=s (time)!
a=m/s2 (acceleration)!
Vector vs Scaler!
5 meters!
5 meters east!
25°F!
55 dollars!
25 miles/hour!
0.3 m/s west!
25 kg!
100 calories!
0.5 m3!
displacement!
distance!
Temperature!
money!
speed!
velocity!
mass!
energy!
volume!
Speed & direction !
velocity!
displacement vs distance traveled!
Find the Resultant !
will it be larger or shorter than the red line?!
5!
3!
Find the Resultant !
will it be larger or shorter than the red line?!
5!
3!
5!
3!
Find the Resultant !
will it be larger or shorter than the red line?!
5!
30°!
5!
3!
3!
5!
3!
Find the Resultant !
will it be larger or shorter than the red line?!
We need to find the x and y components of!
the green line. !
red + blue!
X = 5 + 3 sin 30 = 6.5!
y = 0 + 3 cos 30= 2.6 !
5!
30°!
3!
3!
!
Green arrow = sqrt(6.52+2.62)=7.0!
!
5!
30°!
We need to find the x and y components of!
the green line. !
red + blue!
X = 5 - 3 sin 30 = 3.5!
y = 0 + 3 cos 30= 2.6 !
3!
30°!
!
!
Green arrow = sqrt(3.52+2.62)=4.3!
!
I walk to broadway and up to
72nd st!
12 blocks 'north' !
6 blocks 'west’!
How far did I walk?!
How far am I from where I started?!
What direction did I go in?!
1 mi = 1.609 km= 1,609 m!
20 blocks= 1 mile!
12 blocks north 6 blocks west!
How far did I walk?!
How far am I from where I started?!
What direction did I go in?!
1 mi = 1.609 km= 1,609 m!
20 blocks= 1 mile!
12 blocks north 6 blocks west!
How far did I walk?!
965.4+482.5 m = 1447.9 m!
How far am I from where I started?!
965.4 m!
!
What direction did I go in?!
2 π radians =360°!
θ!
482.5 m!
Θ=arc tan 2 =1.11 radians!
1.11 radians*360° = 63°!
2π !
63° north of west!
cos θ = adj/hyp!
sin θ = opp/hyp!
tan θ= opp/adj!
1 mi = 1.609 km= 1,609 m!
20 blocks= 1 mile!
1 radian = 57.3°!
Draw the vector representation of the trip.!
How far did I walk?!
How far am I from where I started?!
1) I walk 500 m west and go 250 m west!
2) “
“ 250 m east!
3) “
“ 250 m north!
500 m!
2500 m!
Components!
1.0 m/s!
3 m/s!
You are rowing north across the river at 3 m/s!
The current pushes you east at 1.0 m/s!
How fast are you going? 3.16 m/s!
What direction are you traveling? Tan θ = 1.0/3.0 = 18.4°!