The Freefall Slinky: Misconceptions in extended object motion

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```The Freefall Slinky: Misconceptions
in extended object motion
Keith Andrew
Physics and Astronomy
Western Kentucky University
Do the experiment!
Take Physics: Months of buildup as a Viral Video
and a staggering rush on sales
as students become transfixed watching
an object fall to the ground.
Reporter: Derek Muller
Producer: Adam Collins
Researcher: Derek Muller
Camera: Daniel Shaw, Jeff Malouf
Sound: Grant Roberts
Editor: Andrew Glover
Story Contacts
Assoc Prof Rod Cross
Physicist,
University of Sydney
PHYS.ORG: Viral Video Takes Over PHYSICS
Secrets of the 'Levitating' Slinky: Viral
web videos trigger physicists to explore
a striking phenomenon
Physicist’s needs alter national Holiday Shopping trends in Dec. 2012:
While holiday shoppers search frantically for
the Moshi Monsters, LeapPad Explorers, or
Lalaloopsy Silly Hair dolls atop their children's
wish lists, many physicists remain engrossed
in the properties of a simple 1940s-era toy -the Slinky.
Costs less than an iPad!!
The Experiment
Release an extended slinky from rest
so that it is in freefall
towards the ground—
Of course everything
near the surface of the Earth
accelerates at a constant rate
of g=9.81 m/s2
1 2
y   gt
2
Asking the question:
Dr. Derek Mueller and Professor Rod Cross
How will the extended slinky fall towards the ground?
Predict the overall motion of the Slinky.
In particular how does the bottom ring move?
What is a spring?

1
F   kx U s  kx 2
2
x (t )  A cost   
1. M: suspended mass
2. m: spring mass
3. Spring has uniform constant mass density
4. Velocity of each location on the spring is proportional to the length
5. v- velocity of M located at L
m
dm   dy    dy
6. u- velocity of dm located at y
L
L
L
7. Length dy contains mass dm
1 2
1 2  dy 
1m
Physlet from Colorado Demos
E   u dm   u  m 
u 2 dy

2
2
L
2
L
 
0
0
u y

v L
 y
u  v 
L
1 m  vy 
m v2
1m 2
2
 dy  3  y dy   v

2 L 0 L 
2L 0
2 3 
L
E
Effective Mass of Spring
M
7
m
L
M suspended  7mspring
Empirical studies show that
the factor of 1/3 is only valid
up to about 7m (AJP 1970, 38. pp98)
Some Data on Answers
Unofficial survey of 118 web based responses at 13 blog sitesi.e. Protons for Breakfast
No correction or direct knowledge of science background of responders but
a number, 17, were known to be science students and teachers.
Two Categories of answers I did not look at closely:
1. Students worried about being “tricked” yet again by their teacher:
Physics Student to teacher : “ …well if you are asking then it is surely not what
I was thinking…..”
2. Several asked to not anthropomorphize the slinky:
….the Slinky “knows” what to do….
….the Slinky is “smart” enough to…..
….the Slinky coils are “clever” ….
In some sense, many layers
down, I worry a little about
what these responses mean
about science etc. – but not today.
Answers from a Group in the Video
Lady:Ohhhh!
Lady: It wasn’t what I expected.
Assoc Professor Rod Cross
And then I’m going to drop the slinky. But I want you to predict what’s going to happen. Will the top end fall first? Will the bottom end fall first? Or
both ends fall together? Or will the two ends approach each other in the middle?
Dr Derek Muller
That is a tough question. When I let go what does the bottom bit?
Boy
Shoot up.
Man
It’s going to fall. It’s gravity.
Dr Derek Muller
It’s actually going to fall.
Lady
Bottom goes up, top goes down.
Girl
It might come up together.
Man
You’re going see the top come down to the middle and the bottom come up to the top.
Girl
Come to meet it and then drop.
Lady: No, it’s the other way
Man
The top will accelerate faster than the bottom.
Boy
I reckon that bottom will stay there, this will come down to there and then they’ll both fall
Answers Collected in Bins
1. 41% Most Common answer: “the bottom of the spring will move upward…”
Especially for students told to watch the bottom of the slinky.
2. 18% It will all fall
3. It will oscillate and fall and tumble and…
4. Physics fails in this case like the bumble bee….
5. Well the spring constant is related to the fall…
6. The problem is once I see the video it is right out of the cartoons, like Wylie
E. Coyote going over the cliff, he goes straight across and then straight down….
Classroom Center of Mass
Discrete Masses: Sum
Continuous: Integrate
Usually uniform and rigid

rCM 

 rj m j
j
m
j
j


 r dm
 dm
Classroom Extended Object Motion- for a rigid object
CM: Red Dot
1. Motion of CM and
2. Motion about CM


Of  CM :  F j  ma
j
About CM principal  axis :


  I
ccw o
A Simplified Physics Model: 6 Identical Masses Connected by Identical Springs


rCM
r m

m
j
j
j
j
j


r
 dm
 dm
Note: springs are stretched by different amounts- not uniform and not a rigid solid
Tracking Each Mass
Mathematica code is available at several sites
Longitudinal Wave Traveling along the Slinky
Slinky with linear density function
E
Is this what happens…….
1 2 1 2
mv  kx
2
2
Conclusion:
Do the Experiment- get a Slinky- bring it to class.
1.
2.
3.
4.
5.
6.
7.
8.
Measure k of slinky
Did you hear it? Inelastic sound energy is a loss…..
Measure longitudinal wave speed on Slinky: AJP
How long can you make the delay?
Wait- there is a much faster torsional wave: 6 x faster
Use a stiff spring and compare
The collisional wave is a nonlinear shock wavethe top ring would actually Pass the bottom ring….: Unruh.
[1]M. G. Calkin ”Motion of a falling spring”
Am. J. Phys. 63 261 (1993)
[2] See for example
http://en.wikipedia.org/wiki/Shock wave
physics and detonation physics (retrieved
Oct 8,2010)
[3] Unruh arXiv:1110.4368v1
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