General Physics Paradoxes
by
Robert Nemiroff
Michigan Tech
Physics X: About This Course
• Officially "Extraordinary Concepts in Physics"
• Being taught for credit at Michigan Tech
o Light on math, heavy on concepts
o Anyone anywhere is welcome
• No textbook required
o Wikipedia, web links, and lectures only
o Find all the lectures with Google at:
 "Starship Asterisk" then "Physics X"
o
http://bb.nightskylive.net/asterisk/viewforum.php?f=39
Archimedes paradox
Can a large, massive object (like a battleship) float in a tub with
only a little water (say a spoonful)?
1.
2.
3.
Yes.
No.
Only if the water is seawater.
Archimedes paradox
1. Yes.
The key factor is that the average density of the floating object
must be less than the average density of the water it
displaces.
Feynman Sprinkler
A lawn sprinkler sprays water and hence rotates. The lawn sprinkler is
then moved to a bathtub filled with water and hooked up to a vacuum
cleaner. Does the sprinkler spin?
1.
2.
3.
4.
Yes, it spins in the opposite direction than it did on the lawn.
Yes, but it spins in the same direction than it on the lawn.
No, it doesn't spin at all.
This seems easy but I just can't figure it out.
Feynman Sprinkler
1. Yes, it spins in the opposite direction it did on the lawn.
The physics is relatively complex, much more so that the lawn sprinkler
in air. I don't fully understand it myself.
Feynman Sprinkler
In principle, when the sprinkler is turned on, it will accelerate toward the incoming
water. When the water is turned off, it will accelerate in the opposite direction. In
between, when the flow of water is steady, and one assumes that the water is
frictionless, no angular momentum will be transferred so that the sprinkler will
"coast" around.
In practice, however, many sprinklers have high enough internal friction so as to
appear motionless throughout. Also, motion through water has resistance. Some
details of the FS have only been worked out in detail recently.
Tea Leaf Paradox
When you stir a cup of tea with tea leaves, where do the tea
leaves usually end up?
1.
2.
3.
4.
At the bottom, around the edges.
At the bottom, in the center.
At the top, around the edges.
At the top, in the center.
Tea Leaf Paradox
2. At the bottom, in the center.
The paradox has been known informally for a long time. It was solved
by Einstein (!) in 1926.
When stirring, rotation is usually slower at the bottom. This creates a
secondary flow where fluid rises in the center and falls at the
edges. Tea leaves participate in this flow, but are too heavy to become
lifted by the flow at the bottom, and so stay at the bottom center.
The same effect causes erosion of river banks.
Optical Illusion: Shadow paradox
Are squares A and B the same color?
Optical Illusion: Shadow paradox
Are squares A and B the same color?
1. No, square A is darker than square B.
2. Yes, they appear to me to be the same color.
3. This is one of those cases where "maybe" is actually the
right answer.
Optical Illusion: Shadow paradox
2. Yes, they appear to me to be the same color.
Moon Illusion
Does the Moon appear larger
when it is viewed near the
horizon?
1. Yes.
2. No.
3. Is the Moon the one that looks like an orange or the one that
looks like pizza?
Moon Illusion
2. No.
The reason for the
illusion is still being
debated. Factors
discussed include
that objects near the
horizon appear behind other objects and hence appear further
away, and that objects appearing near other objects of smaller
angular size appear larger.
Freezing Water Paradox
True or False: Under some circumstances, warm water will
freeze faster than cold water.
True: Some freezers just do this.
False: The warm water must cool first to the temperature of the
cold water before freezing, therefore, it takes longer to freeze.
Mpemba Effect:
Freezing Water Paradox
True: Some freezers just do this.
Why? I like this example because it shows how the complexity of the
real world can complicate even simple physics experiments.
Mpemba Effect:
Freezing Water Paradox
Possible reasons include:
•
•
Evaporation: more warm water will evaporate before freezing,
leaving less to freeze
Warm water will melt more of the surrounding freezer frost, then
exposing the water to the colder sides
Mpemba Effect:
Freezing Water Paradox
Also:
•
The temperature pattern in the water may differ between the
initially cold water and the warm water cooled to the cold water's
initial temperature. Cold water may freeze from the top and
insulate itself. Warm water may freeze from the bottom without
the insulating effect of a top layer of ice.