Mec E 415 Busting Myths with Analysis
Winter 2012 - January 9 to April 13
Instructor: Jason Carey,
Class time: TR 11:00-12:20
Mec Eng 5-8T, 492-7168
MecE 4-16
Thursday 2-3PM, Open door policy
or by appointment
[email protected] and Skype contact (email to request meeting) jcarey.ualberta.ca
Prerequisites: Mec E 330, 340, 370, 380, 390, Math 300.
Marking scheme:
Assignments
In class participation
Midterm
Final exam
“Bust your own myth” project
Due/scheduled
In class, TBD on progress
Thursday Feb 16 in class
9:00 am Thursday April 26
last class April 12
Worth
15%
10%
15%
40%
20%
Text and References: No textbook will be required.
Website: Eclass
University Policies
Policy about course outlines can be found in §23.4(2) of the University Calendar.
The University of Alberta is committed to the highest standards of academic integrity and
honesty. Students are expected to be familiar with these standards regarding academic
honesty and to uphold the policies of the University in this respect. Students are
particularly urged to familiarize themselves with the provisions of the Code of Student
Behavior (online at www.ualberta.ca/secretariat/appeals.htm) and avoid any behavior
which could potentially result in suspicions of cheating, plagiarism, misrepresentation of
facts and/or participation in an offence. Academic dishonesty is a serious offence and can
result in suspension or expulsion from the University
Class format:
Introduction of the class will be an interactive discussion of the myth being tackled.
Students will be provided at the beginning of the course the list of myths to be
undertaken, the information pertinent to the myth; they will be required to be prepared for
lectures. Each lecture will begin with the question: myth possible or not, and why? This
is to emphasize engineering intuition and understanding of physical phenomena.
Following the discussion period the instructor will provide a solution, often the simplest
one, required to bust or prove the myth.
Become a professor for part of a lecture: propose a new myth (can be your project
myth) and present it as a teacher to the class– doing so gives an automatic 10/10 for in
class participation marks. The instructor must approve the myth and proposed lecture
material. Presentation must be between 25 and 35 minutes, provide background
information, use the proper teaching medium, and have an engineering approach and
solution.
Prof: J. Carey
1
Mec E 415 Busting Myths with Analysis
Project:
Find a myth (not one done in class and not from previous years) and validate or bust.
The project requires a short report (5-10 pages max including analysis) that includes:
• Myth background
• Pertinent information
• Pertinent theory and assumptions
• Analysis of the myth
• Discussion of the important elements of the myth; could it be solve differently; what
could make it plausible or busted; etc.
• Conclusion
• References
Course Objectives:
Core courses taken by undergraduate students provide an excellent knowledge of the
basic theoretical considerations that are used to address standard textbook problems.
However, it can be a major leap to apply this knowledge to more complex multi-faceted,
multidisciplinary problems that include high level analysis and synthesis. Synthesis is a
major part of most technical engineering work, and so it is important for our students to
develop proficiency in this regard. The capstone design course (Mec E 460) does provide
some exposure to more advanced synthesis, but this exposure is limited to the single
design problem being considered by the student’s group.
In this course, synthesis will be used to examine approximately 25 complex engineering
problems that involve advanced multidisciplinary theoretical analysis, giving the students
excellent exposure to the synthesis process while at the same time honing their analysis
and theoretical skills. While much of the necessary theory will be drawn from material
the students have taken in previous courses, the complexity of the problems being
considered will require a reasonable amount of new theoretical knowledge presented in
the context of the course.
In order to maximize student engagement in the course, each problem being considered in
class lectures will have a commonly held scientific or technological myth upon which
synthesis and analysis is used to bust or confirm the myth under consideration. Some of
the myths will be drawn from those examined in episodes of the popular TV show
“Mythbusters”, allowing comparison of results obtained in class using theoretical
methods to those obtained experimentally on Mythbusters. The remainder of the myths
will be drawn from commonly held myths in engineering practise, public misconceptions
and urban legends. The course will thus expand the students’ synthesis and analysis
skills, while at the same time reinforcing and expanding their theoretical knowledge and
providing them with knowledge regarding the veracity of commonly held engineering
and scientific myths and misconceptions.
Prof: J. Carey
2
Mec E 415 Busting Myths with Analysis
Myths
Lecture Topic
1.
Introduction to course (outline, objectives, schedule…)
Short myths: Race car drive up-side-down
2.
Run or walk in the rain/ Run or walk in the cold
Airborne myths
3.
Plane on conveyor belt; Penny dropped from building is deadly
4.
Water bottle jet liftoff
5.
Border slingshot
6.
Using a bomb blast to land safely from freefall without a parachute
7.
Birds on a truck will lighten the load if they fly
8.
Exploding pressurized balloons used for lawn chair flight
9.
Swing set straight 360
Gun Myths
10. • Introduction to bullet info, how bullets work
• Poncelet’s approximation to bullet penetration (Ie why is 40m/s deadly or
how ballistic gel is used)
• How long is a bullets lethal for
• Ice bullet
11. Under water bullet shelter
12. Bullet and guns in oven are deadly
13. Blown away (cowboy myth)
14. Bullet shot vertically deadly?
15. Bullet deviating magnetic watch
Car myths
16. Cable pulls off car axle
17. Drive shaft pole vault
18. Skidding straight or turn to avoid a wall collision
Pressure vessel myths
19. Compressed air cylinder can power a boat
20. Compressed air cylinder can break through a cinder block wall
21. Exploding/rocket water heater
22. Pop can explode if left in car (hot and cold)
Other myths (not all will be done, others substituted)
23. Break step bridge
24. Twin tower conspiracy myth
25. Bath tub vortex always rotates counter clockwise
26. Brachristochrone
27. Faster to freeze hot water bucket than cold one
28. Beer cooled (ice water, Salt ice water, fire extinguisher, fridge, freezer, sand +
quart of gas)
Prof: J. Carey
3
MecE 415: Assignment problems
A.
Intro myths
Run versus walk in the rain
Revisit the run vs walk in the rain myth when
1. a constant head wind is present
2. a constant crosswind is present (i.e. Vy≠0)
3. a constant tailwind is present (tough problem)
Run versus walk in the cold
Revisit the run vs walk in the cold myth when
1. a constant head wind is present
2. a constant crosswind is present (i.e. Vy≠0)
3. a constant tailwind is present (tough problem)
B.
Airborne myths
Penny drop myth
1. Reconsider the penny drop myth where a toonie is dropped instead of penny. Use
d=28mm, m=7.3g for a toonie.
2. Reconsider the penny drop myth where a quarter is dropped instead of penny.
Use d=23.88mm, m=4.5g for a Canadian quarter.
3. Reconsider the penny drop myth where a one ounce Maple Leaf Gold coin is
dropped instead of penny. Use d=30mm, m=31.1g for a toonie.
Water bottle rocket myth
1. Reconsider the water rocket myth example with the bottle exits reduced to 1cm
diameter. Assume a gauge pressure of 1000kPa, 2 liter bottles and a 1.2 liter fill.
(requires numerical ODE solver)
2. Reconsider the water rocket example in class with an assumption that the pressure
in the rocket chamber is constant, so t hath the exit gas velocity Ve is constant. In
this case show that the rocket velocity will be

m 
Vr (t )  Ve ln1 
t   gt
 m0 
dm
is the constant mass flow rate of water leaving the rocket.
dt
3. Redo water rocket example in class with 2 litre bottles filled half full. Use an
initial fill pressure of 500,000Pa. (requires numerical ODE solver)
Where m 
Winter 2010
J. Carey
1/6
MecE 415: Assignment problems
Border slingshot
1. If we do not consider drag at all (or death by impact), is this more plausible?
2. What is the influence of angular velocity? Assume =0
3. For the myth we assumed a 45º launch angle gives the furthest horizontal distance
travelled; however this is only true if there is no drag. Revisit the myth using
Us=42,500J and all other information previously provided and find the optimal
launch angle. How much further will the dummy go at this launch angle?
22,000 foot drop
1. Assuming a blast wave wind speed of 65m/s, which is the highest possible value
to avoid injury, what size bomb blast would be needed to slow a person’s fall
velocity to 10m/s? Use the parameter values from class and the blast wind
duration is =0.0015 3  .
Exploding pressurized balloons used for lawn chair flight
1. Revisit the myth using MecE 380
pressure vessel theory and strain
energy failure criterion assuming
the given linear elastic
properties. If we remain at sea
level, what is the internal
pressure required to fail the
balloon and what is the final
internal volume?

Sut=5MPa
2. Comment on the results

f=0.20
Swing set 360
1. Almost everyone who has sat on a swing set as an adult knows that most swing
set pivot point moves when swinging (proof that we are too big for them). If we
assume the chain is rigid and that the pivot moves following x p  A sin(t ) , what
is the equation of motion?
2. A circus performer showed that it was easier to do a 360 if the chain is rigid.
What is the minimum velocity at the bottom of the swing required to get a full
rotation assuming no losses in the system? Assume the distance between the
person’s CG and the pivot is 1.5meters.
Winter 2010
J. Carey
2/6
MecE 415: Assignment problems
C.
Gun Myths
Ice bullet
In the ice bullet myth, if we suppose the bullet exits the gun undamaged, it will
undergo friction from the drag forces which will heats the bullet. The frictional
energy is given as:
C AV 2
(Mega Joules per km) if the flow is turbulent.
E friction  d
1000
drag
For a 9mm bullet, assuming constant velocity and an initial bullet temperature of 150ºC, how far will the bullet travel before completely melting? Show that the
flow is turbulent.
Under water bullet shelter
1. How far underwater do you need to be to not have skin penetration of a bullet
fired from a 0.22 long rifle with m=2.0g, d=5.7mm and muzzle velocity 440m/s.
2. The mythbusters used a 3” deer slug in a shotgun (the length is 3”) but broke the
test tank and could not determine how deep the slug penetrated. Estimate the
distance underwater you would need to hide to prevent a 3” deer slug from
penetrating your skin. Assume a 28g mass, a diameter of 18.5mm and a muzzle
velocity of 500m/s which is typical of a 3” magnum shell in a 12 gauge shotgun.
Use Cd for flow past a blunt nosed cylinder.
Bullet and guns in oven are deadly
Revisit the myth with a 50-caliber bullet. Is the bullet deadly on its own?
Blown away (cowboy myth)
1. What mass would an object shot at need to be if it was to travel back 3.1 meters
assuming the bullet was imbedded and the mass was 1 meter of the ground at
impact?
2. Revisit the myth with a 9mm bullet (mb=0.009kg) and Vm=360m/s.
3. If a person was running away from the shooter at 3.1m/s how far would he be
blown away if shot with the 50 cal?
Bullet shot vertically deadly?
1. In the myth we assumed drag was negligible on the way up. What would be the
altitude the bullet reaches if we do not neglect drag?
2. Reconsider the myth for a 50-cal, is it lethal if shot vertically?
3. Reconsider the bullet fired upward at an angle for a Winchester 0.458 Magnum
having mb=32g, V0=600m/s, db=11.6mm, Cd=0.3 and =45º. Determine the
horizontal distance travelled and the speed at impact. Is this lethal?
Winter 2010
J. Carey
3/6
MecE 415: Assignment problems
Bullet deviating magnetic watch
1. How much magnetic force would be required to pull the bullet down 2cm over a 1
meter distance?
2. Over a bullet’s entire trajectory, what would be the change in range if there were a
magnet with the same force placed all along the path on the ground, if it is shot at
a height of 1.5 meters?
D.
Car myths
Cable pulls off car axle
1. Find a bolt configuration for a car and perform pull off analysis
2. Why would the cable not break if tight at t=0 as in the case of a winch? What
would be the likely result (prove your answer using analysis)
3. What is the stress in the cable wrapped around the axle and post if dw = 1” and
dpole=8”?
Drive shaft pole vault
1. Revisit the drive shaft pole vault myth and assume the drive shaft could have
buckled. Using Pcritical for impulse, how high would the back end lift?
2. Do the same using the force from the compressive strength.
Skidding straight or turn to avoid a wall collision
1. For V0=10m/s, =0.15 (tires on ice), r=10m, d=5m impact occurs at tc=0.543sec
for the curved path. Compare the speed of impact for the straight and curved
path.
2. For V0=10m/s, =0.7 (tires on asphalt), r=10m, d=5m impact occurs at
tc=0.656sec for the curved path. Compare the speed of impact for the straight and
curved path.
3. For V0=20m/s, =0.15 (tires on ice), r=10m, d=5m impact occurs at tc=0.543sec
for the curved path. Compare the normal impact speed Vcg=V(tc)cos of the
curved path to the straight path impact impact speed Vc.
E.
Pressure vessel myths
Compressed air cylinder can power a boat
1. Find the velocity of the compressed air boat from class using an exit nozzle
diameter of 2mm.
2. If the tanks are pressurized to 5000psi, the boat travels at its maximum speed of
V=3.3m/s for a displacement hill boat. Give an estimate of the distance travelled.
Assume a 10kg charge to each tank.
3. Find the velocity of the compressed air boat with helium as the compressed gas
and all other variables used in the class. Use k=1.66, R=2077m2/s2K
Winter 2010
J. Carey
4/6
MecE 415: Assignment problems
Compressed air cylinder can break through a cinder block wall
1. Revisiting the myth, how much time would it take for the tank to be empty? What
would be the distance travelled when it is empty? How far would a person need to
be to not get hit if the friction coefficient between tank and floor is 0.1 once it is
no longer propelled?
2. The myth revolved around the question is this impact lethal for people. Show that
the impact of the cylinder with a human body (assume in the abdomen) would
hurt.
Pop can explode if left in car (hot and cold)
1. At what temperature increase will the can tab fail? Water’s compressibility is
0.46/GPa. Assume T1=4ºC
2. What would be the strain state at yield failure pressure 1.57MPa
3. Cans used to be, and still are in some countries, made of stainless steel. What
would be the pressure required to pop the tab if the dimensions are the same?
Ss=350MPa
Exploding/rocket water heater
1. After plowing through the ceiling, how high would the tank go if we consider
drag?
2. If we don’t consider drag?
3. Could the tank go two floors? Assume the 2nd impact occurs at V=148.7m/s and
impacts with a force of 24900N over 0.1 secs
4. How many wooden floors could it go through?
F.
Other myths
Brachristochrone
1. Consider a soap film that bridges two circular hoops as shown. The film is a
surface of revolution obtained by rotating the
x
curve y(x), that passes between the two fixed
y(x)
end points (x1,y1) and (x2,y2), about the y(x1,y1)
axis. The soap film will take on a shape such
(x2,y2)
that the surface area is minimized since this
minimizes the surface energy. Use analysis to
confirm or bust the myth that the soap film
y
will be a truncated cone.
2. Use the calculus of variations to show that the shortest distance between two
points in a plane is a straight line.
Winter 2010
J. Carey
5/6
MecE 415: Assignment problems
A pail of hot water freezes faster one of room temperature when in cold
1. Compare the relative time for a pail of 70ºC water to freeze versus a 20ºC pail of
water by using the analysis given in class with ambient T=-10ºC.
2. Compare the relative time for a pail of 90ºC water to freeze versus a 20ºC pail of
water by using the analysis given in class with ambient T=-20ºC.
3. Compare the relative time for a pail of 50ºC water to freeze when the ambient
T=-10ºC versus when the ambient T=-20ºC.
Break step Bridge
1. What are the natural frequencies if the length of the bridge, l, is 5600ft?
2. If the failure strength of the cable is 72.5kpsi, what would be the maximum load
on the floor that the bridge could support if the cables are 17in in diameter?
Twin tower conspiracy
1. What mass would have needed to hit the towers to cause the base to go into the
plastic deformation range (Limit Sy=250MPa) and fail leading to a possible
scenario of the tower falling like a tree if we assume as Roark stipulates that the
impact stress is found by:
 i di
VI2


 n dn
gd n
Where n and dn are the nominal stress and deflection caused by an equivalent
static load. The plane hit at 340m. Assume offset of centre of gravity is
negligible.
2. What would be dI and dcg if our assumption is correct? (Mass of towers is 188x106
kg)
3. Find the required mass of the plane without making the above assumption.
4. It is desired to confirm that the column structure could support the mass of the
tower in pure compression if it is made up of 44 core columns (14”x36” outer
dimensions with 1” wall thickness) and 59 side columns (14”x14” outer
dimensions with 1” wall thickness) on each side (no repeats). It is estimated that
a tower weighs 188x106 kg. The columns must not yield (E=200GPa, Sy=
250GPa)
Winter 2010
J. Carey
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