General Physics Paradoxes

byRobert NemiroffMichigan 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 requiredo Wikipedia, web links, and lectures onlyo 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. Yes.2. No.3. 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. Yes, it spins in the opposite direction than it did on the lawn.2. Yes, but it spins in the same direction than it on the lawn.3. No, it doesn't spin at all.4. 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. At the bottom, around the edges.2. At the bottom, in the center.3. At the top, around the edges.4. 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 includethat objects near thehorizon 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.