desert island survival physics...

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



SACS AAPT Fall 2014

ABSTRACT

Phone: 843-437-1640 [email protected]

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



SACS AAPT Fall 2014

Perfect tool versus bare hands



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



SACS AAPT Fall 2014 Brewing tea

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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?



SACS AAPT Fall 2014

Height by triangulation

Height by triangulation



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⎡ ⎤= − − −⎣ ⎦



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



SACS AAPT Fall 2014

Applying what you learn in one field to another one

Learn how to see similarity in things looking absolutely different

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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= +



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



SACS AAPT Fall 2014

Jigsaw puzzle mentality



SACS AAPT Fall 2014

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