Download MythBusters For High School Physics

MythBusters For High School Physics
© http://www.real-world-physics-problems.com
April 2015
Email: [email protected]
Alternate email: [email protected]
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Description of Content
Content suitable for introductory high school physics courses is denoted by the text
"Introductory Level" placed beside each topic. Content suitable for advanced high school
physics courses (such as Advanced Placement Physics) is denoted by the text "Advanced
Level" placed beside each topic. Note that the introductory level topics can also be used
as course material for advanced courses, as deemed suitable by the instructor.
The topics in this ebook are taken from select episodes of the Mythbusters television
show. The topics chosen lend themselves well to a physics analysis. The topics, in
general, do not fit neatly into individual and separate concept groups. This is the norm
when analyzing and solving real-world problems. This forces you to draw on your own
knowledge and experience in a way that end of chapter textbook problems do not. And in
so doing it challenges you to think in broader scientific and engineering terms, which fits
well with the spirit of, say, the Next Generation Science Standards being adopted by K12 schools in the United States.
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Contents (organized chronologically by episode)
Advanced Level - Is running better than walking to keep dry in the rain? (2003 season,
episode 1) - Page 5
Advanced Level - Can a standard CD-ROM drive shatter a CD? (2003 season, episode 2)
- Page 7
Advanced Level - Will a penny dropped from the top of the Empire State Building kill a
person or penetrate the ground? (2003 season, episode 4) - Page 8
Introductory Level - Do frozen chickens cause more damage than thawed chickens when
shot at a plane's windshield? (2004 season, episode 10) - Page 11
Introductory Level - Can mirrors be used to make a death ray? (2004 season, episode 16)
- Page 11
Introductory Level - Can someone survive a multi-story elevator fall by jumping right
before the elevator hits the bottom of the shaft? (2004 season, episode 17) - Page 12
Introductory Level - Is it possible to make a hovercraft with a vacuum motor? (2004
season, episode 17) - Page 12
Introductory Level - If someone falls off a building, can that person glide to safety using
a sheet of plywood? (2004 season, episode 18) - Page 16
Introductory Level - How many balloons are needed to lift a 40-lb child off the ground?
(2004 season, episode 21) - Page 16
Introductory Level - Do free energy devices seen on the Internet actually work? (2004
season, episode 24) - Page 17
Introductory Level - Does a clothed snowman melt slower than a "naked" one? (2004
season, Special 1) - Page 17
Introductory Level - Can a urine stream freeze in the winter? (2004 season, Special 1) Page 17
Introductory Level - Can a person be blown away by a bullet? (2005 season, episode 25)
- Page 17
Introductory Level - Does buttered toast always land buttered side down? (2005 season,
episode 28) - Page 18
Introductory Level - What is the fastest way to cool a six pack of beer? (2005 season,
episode 29) - Page 18
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Introductory Level - Will diving underwater protect a person from bullets? (2005 season,
episode 34) - Page 18
Introductory Level - Will a black car heat faster than a white one? (2005 season, episode
38) - Page 19
Advanced Level - Can a football fly farther if it is filled with helium? (2006 season,
episode 47) - Page 19
Introductory Level - Can a bullet fired straight up in the air kill someone on the way back
down? (2006 season, episode 50) - Page 22
Advanced Level - Do birds flying in a trailer cause the trailer to become lighter? (2007
season, episode 77) - Page 22
Introductory Level - Can fuel be saved by tailgating a semi-trailer truck? (2007 season,
episode 80) - Page 23
Introductory Level - Can dry balls be hit farther than humid ones? (2007 season, episode
83) - Page 24
Introductory Level - Can balls be hit further with a corked bat? (2007 season, episode 83)
- Page 24
Advanced Level - Can a water heater explode like a rocket and shoot through the roof of
a house? (2007 season, episode 89) - Page 24
Introductory Level - If a person jumps out of an airplane with the last parachute, can
another person jump out later and catch the person? (2007 season, episode 94) - Page 25
Advanced Level - Does a 4,000 foot fall take 90 seconds? (2007 season, episode 94) Page 25
Advanced Level - Can a watch-sized electromagnet deflect a bullet? (2008 season,
episode 95) - Page 26
Introductory Level - Can a lead balloon fly? (2008 season, episode 96) - Page 27
Introductory Level - Can an airplane take off while on a conveyor belt? (2008 season,
episode 97) - Page 28
Introductory Level - Will a feather and a hammer drop at the same rate in a vacuum?
(2008 season, episode 104) - Page 28
Introductory Level - Could the flag have flapped like it did on the moon? (2008 season,
episode 104) - Page 28
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Advanced Level - Is it possible to lift a car using fire hoses? (2008 season, episode 105) Page 29
Advanced Level - Are two interlaced phone books impossible to pull apart by any
means? (2008 season, episode 106) - Page 30
Advanced Level - Will a motorcycle flip if a pole is thrust into the front wheel? (2008
season, episode 111) - Page 32
Advanced Level - When a bus is moving at over 50 miles per hour, will moving
passengers to the inside of the turn keep the bus from flipping? (2009 season, episode
114) - Page 34
Advanced Level - Will a car dropped from 4,000 feet fall faster than a speeding car?
(2009 season, episode 114) - Page 37
Advanced Level - Did Hungarian archers get twice the penetration shooting a bow from a
galloping horse? (2009 season, episode 119) - Page 39
Advanced Level - Could a skydiver whose parachute failed to open hit a playground
seesaw and send a small girl flying seven stories high, and she could still survive? (2009
season, episode 120) - Page 40
Advanced Level - Why are dimples crucial to the flight of golf balls? (2009 season,
episode 127) - Page 42
Introductory Level - Can a bottle of beer, when given a sudden shock, turn from a liquid
and freeze into a solid? (2010 season, episode 153) - Page 43
Introductory Level - Can a car's tire pressure affect its fuel efficiency? (2010 season,
episode 153) - Page 43
Advanced Level - Can a sailboat stranded in calm water start moving by blowing air into
its sail with an onboard fan? (2011 season, episode 165) - Page 44
Introductory Level - Will a super-sized Newton's cradle work? (2011 season, episode
172) - Page 44
Advanced Level - Can you use a whip to swing safely across a chasm? (Indiana Jones)
(2015 season, episode 224) - Page 45
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Advanced Level - Is running better than walking to keep dry in the rain? (2003
season, episode 1)
Model the person as an upright rectangular box moving through the rain at speed V as
shown. The surface (1) represents the front of the person and the surface (2) represents
the top of the person.
(2)
(1)
V
The figure below shows a side view of the set up. Assume that the rain is falling straight
down.
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w2
(2)
w1
(1)
V
Let w1 be the rate of rain impingement on the front of the person (given as volume of
water per second). Let w2 be the rate of rain impingement on the top of the person (given
as volume of water per second).
If the person is standing still w1 = 0. If the person is moving then w1  0. The faster the
person moves (at greater speed V) the greater is w1.
The rate w2 is always the same whether the person moves or not.
The rate w1 is proportional to V. Mathematically this means that w1 = aV, where a is a
constant.
Let's say the person has to travel a distance d through the rain. We have to determine if
this person should walk or run. The total amount (volume) of water that impinges on the
front of the person as he/she travels the distance d is equal to A1 = w1T, where T is the
total time (in seconds) it takes for the person to travel the distance d to their destination
Now, T = d/V, therefore A1 = w1(d/V) = aV(d/V) = ad, which is constant. Now, the total
amount of water impinging on the person is A1 + A2, where A2 is the amount (volume) of
water impinging on the top of the person, and A2 = w2T. Since A1 is constant, then to
minimize getting wet we must minimize A2. Since w2 is always the same no matter what
V is, then to minimize A2 we must minimize the time T spent in the rain. Therefore to
minimize getting wet the person must run as fast as he/she can to their destination.
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Advanced Level - Can a standard CD-ROM drive shatter a CD? (2003 season,
episode 2)
A CD can be treated as an annular disk with inner hole radius a and outer radius b. The
maximum stress occurs at the inner hole location at radius a. This is the part of the CD
that will break first if it is spun too quickly. As the disk spins centripetal forces are
generated inside the structure of the CD and these forces are what put the CD material
under stress. If the stress is too great (due to the CD spinning too fast) the CD will break.
Maximum stress location. For visualization
purposes this is illustrated with a differential
element shown to be in tension
t
t
b
a
w
Assume the CD has no cracks or flaws in it, which would complicate the analysis.
The maximum stress of the rotating CD is located at the inner hole location (at radius a).
This stress is tensile. At this location the stress is given by the following solid mechanics
equation:
3   2 2   1   a 2 

t  
 w b 1  
 2 
 4 
  3   b 
Where:
t is the tangential stress, which acts as tension in the circumferential direction. The
maximum tensile yield stress which can be withstood by CD material (polycarbonate
plastic) is roughly 65x106 pascals (newtons per square meter).
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 is the Poisson's ratio for the CD material, which is 0.37
 is the density of the CD material, which is 1200 kg/m3
w is the angular velocity of the CD, in radians per second. This quantity must be
determined
b is the outer radius of the CD, which is 0.06 m
a is the inner hole radius of the CD, which is 0.0075 m
Now solve for w. We get w = 4220 radians/second. This is equal to 40,300 RPM. This is
well above the maximum rotational speed of CD-ROM drives which may top out at about
24,000 RPM. Therefore a standard CD-ROM drive cannot shatter a CD.
Advanced Level - Will a penny dropped from the top of the Empire State Building
kill a person or penetrate the ground? (2003 season, episode 4)
The fastest speed a penny can achieve is terminal speed. This is the speed at which the
drag force from air resistance exactly balances the force of gravity pulling down on the
penny. As the penny falls it accelerates until its speed is high enough so that the
corresponding air drag force exactly balances the force of gravity pulling down on the
penny.
Consider the schematic showing a penny falling with the thin side facing down. This
orientation results in the greatest terminal speed, as will be explained.
v
g
D
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The general equation for the drag force acting on a body is:
1
D  CAv2
2
Where:
D is the drag force acting on the body
C is the drag coefficient, which can vary along with the speed of the body. But typical
values range from 0.4 to 1.0 for different fluids (such as air and water)
ρ is the density of the fluid through which the body is moving (in this case, the fluid is
air)
v is the speed of the body relative to the fluid
A is the projected cross-sectional area of the body perpendicular to the flow direction
(that is, perpendicular to v). This is illustrated in the figure below.
v
projected
area
The force of gravity pulling down on the penny is:
W  mg
Where:
W is the force of gravity pulling down on the penny
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m is the mass of the penny
g is the acceleration due to gravity, which is 9.8 m/s2
When terminal speed is reached D = W so we have
1
mg  CAv2
2
Set v = vt and solving for terminal speed we have
vt 
2mg
CA
An important observation is that, the smaller the cross-sectional area A, the higher the
terminal speed. The minimal value of A occurs when the penny is falling with the thin
side facing down. In reality the penny will likely tumble through the air but in the interest
of testing the validity of this myth we shall assume a "best case" scenario in which the
penny is falling at the fastest possible speed.
We have the following values for a U.S. penny:
m = 0.0025 kg
diameter = 0.019 m
thickness = 0.0015 m
A = diameter x thickness = 0.019 x 0.0015 = 2.85x10-5 m2
 = 1.2 kg/m3 (density of air)
C = 0.5 (crude approximation based on drag coefficient for sphere as shown on
http://en.wikipedia.org/wiki/Drag_coefficient)
Using the above values we get vt = 54 m/s which is 190 km/h. Although high, this would
not be enough speed to kill a person, or even badly injure them. But it would definitely
hurt! It would also not be enough speed to penetrate a concrete surface. And keep in mind
that this is the highest possible speed. The penny, as it tumbles through the air, spends
some time in different orientations which produce a greater value of A, thus resulting in a
lower terminal speed than the one calculated here.
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Introductory Level - Do frozen chickens cause more damage than thawed chickens
when shot at a plane's windshield? (2004 season, episode 10)
Yes they do because they are harder. It's like throwing a tennis ball at a wall versus a rock
(both having the same mass and thrown at the same velocity). The rock will do more
damage since it's harder. You can think of this in terms of the impulse and momentum
equation: Ft = mv2  mv1, where F is the average force during the impact, t is the time
duration of the impact, m is the mass of the object, v1 is the object velocity before impact,
and v2 is the object velocity after impact. The right hand side mv2  mv1 is the change in
momentum of the object, during impact, which can vary somewhat depending on the
hardness of the object. But the biggest effect of hardness is on t which becomes much
smaller as an object becomes much harder. This means the force F must increase by a
large amount to produce a similar change in momentum during impact. Hence, a harder
object results in a larger F, and causes more damage during impact.
Introductory Level - Can mirrors be used to make a death ray? (2004 season,
episode 16)
Yes. By using a large number of mirrors, with adjustable orientation, a death ray can be
created. For example, a solar power tower
(http://en.wikipedia.org/wiki/Solar_power_tower), which uses the sun's energy to
produce electricity, uses many mirrors to focus concentrated sunlight onto a central
receiver. This receiver then becomes very hot as a result. A control mechanism is used to
track the position of the sun and orient the mirrors accordingly so that they each reflect
sunlight onto the central receiver. Alternatively, this control mechanism can be used to
focus concentrated sunlight anywhere you want, such as at an enemy. The only drawback
is that it can't be used at night or when it's cloudy.
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