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Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
Physical Sciences Department Trident Technical College
Charleston, SC
Charleston, SC October 24 – 25 , 2014
Desert Island Survival Physics 101.
Physics Department The Citadel
Charleston, SC
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
ABSTRACT
Phone: 843-437-1640 AgrestM@CofC.Edu
http://www.cofc.edu/~agrestm
Mikhail M. Agrest, Ph.D. Physical Sciences Department.
Trident Technical College Charleston. SC.29424
“Give me a fulcrum and I will move the world” - shouted Archimedes, finding a perfect solution. Which is the best? A solution implemented with a perfect tool, or the Desert Island Survival Solution – one, executed with bare hands? A student stuck at a Desert Island on her way back from the Spring Break. Being inspired by her teacher’s solving problems via reasoning from the conceptual principles all the way to the answer; she did come up with a result without the unavailable Internet, but had an error that led to an incorrect answer. Another student based his answer on the information acquired from the Internet. Just a few steps led to the absolutely correct solution. Which work you would assign a higher grade? The author will share some examples of providing unnecessary information as well as examples of how to find solutions from limited, but sufficient conceptual information [1,2]. 1. M. Agrest. Lectures on Introductory Physics I and II. 249 pp. and 252 pp. with illustrations Thomson Learning. ISBN 1426625596, 2007, ISBN 0-759-39304-4, 2006 2. M. Agrest. Lectures on General Physics I and II. 257 pp. and 237 pp. with illustrations. Thomson Learning. ISBN 0-759-35047-7, ISBN 0-759-36060-X, 2005
Mikhail M. Agrest, Ph.D. Physics Department
The Citadel Charleston, SC 29409
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
Perfect tool versus bare hands
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014 Volume of the blue rubber ball
2 2 2
0 0
3 3 32 3 3
03 3
2 2
02 2 03 3 3
2 423 3
r r
r
V x dy r y dy
y rr y r
r r
( )π π
π π
ππ
= ⋅ = ⋅ − =
⎡ ⎤⎡ ⎤ ⎛ ⎞ ⎛ ⎞= − = − − − =⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠ ⎝ ⎠⎣ ⎦
= =
∫ ∫
Mathematician Physicist Engineer
Handbook of blue rubber balls
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014 Brewing tea
A Mathematician and a Physicist Case One Case Two
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014 Radius of the Earth
From the map you estimate the distance to the opposite side of the lake as d=6.1 km. Why not Google for the Radius of the Earth? Why not use what you learn from the previous example?
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
Height by triangulation
Height by triangulation
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
One dimensional motion with the constant acceleration
y y
a const
x t x V t a t
v t v at
x x t V t a t
x t xv a tt
v v t atv t vat
v v g y tt
g
20 0
0
20 0
00
0
0
20 0
1( )2
( )1( )2
( ) 12
( )( )
2 ( )
= ⇒
⎫= + + ⋅ ⎪
⎬⎪= + ⎭
= − − ⋅
−= − ⋅
= −
−=
± − ⋅=
( ) ( )t x x y yg 0 02 tanθ⎡ ⎤= − − −⎣ ⎦
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
Atwood’s Machine
2 1
1
1 22
1
0 0222
m m
a gmmmT g m gm
= ⇒
= =
= =
( )( )
( )
2 1
1
1
1
1
00
2 0 00
m mm
a g gmmT gm
⇒
−= = −
+
×= =
+
=
+T −m1g = m1am2g −T = m2a⎧ ⎨ ⎩ ⎪
T −m1g +m2g −T = m1a +m2ag m2 −m1( )= a m1 +m2( )⇒
acceleration : a = gm2 −m1( )m1 +m2( )
T1 T2
T1
T2
m1g m2 g
T = m1a +m1g = m1 a + g( );
T = m1 gm2 −m1( )m1 +m2( )
+ g⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ ⇒
T = gm2 −m1( )m1 +m2( )
m1 +m1⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
T = g m2 −m1( )m1 +m1 m1 +m2( )m1 +m2( )
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ ⇒
T = g 2m1m2m1 +m2( )
( )( )
( )
2 1
2
2
2
2
002 0 00
m mm
a g gmmT gm
⇒
−= =
+
× ×= =
+
?
2.9
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
Applying what you learn in one field to another one
Learn how to see similarity in things looking absolutely different
Learn how to see difference in things looking absolutely same
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
HARMONIC OSCILLATOR vmax = v0 xmax = x0 Hook’s Law:
⇔−=⇒⎩⎨⎧
=
−=x
mka
maFkxF
⇒= 2ωmk
xkt x
t m
Δ⎛ ⎞Δ⎜ ⎟Δ⎝ ⎠ = −Δ
2
xt xt
ω
Δ⎛ ⎞Δ⎜ ⎟Δ⎝ ⎠ = −Δ
;22kmT π
ωπ==
mk
Tf
π211
== natural frequency
( )cosx A tω φ= +
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
SIMPLE PENDULUM
mg cos θm
mg
mg sin θ
θ
θ
S
L
T
s mgF mg F mg sL LF mg
mgs
LL
m mT mgkL
LTg
kxsmall
where k=
sin
2 2
2
θ
θ θ
θ
π π
π
⎫⎪= − ≈ − = − = −⎪
⇒ ≈ − ⇒⎬⎪⎪=⎭
= = ⇒
= ⇒
gfT L
natural frequency1 12π
= =
Hertz
111 1 −= = =Hz ss
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
Jigsaw puzzle mentality
Copyright 2014 © M. AGREST
Desert Island Survival Physics 101 M. Agrest
SACS AAPT Fall 2014
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