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Exacting Nuts
(for exacting humans only?)

 

In a lake, a swimmer is crying for help. A member of the rescue party hastens to the rescue in the shortest time possible. Knowing he runs four times as fast as he can swim, and knowing the shortest route to the person at need runs along a straight line which is not perpendicular to the waterside, what will he do?

[ Fermat ]

1. He takes the shortest route.
2. He minimizes the distance he's going to swim.
3. He uses the principle that underlies the way light travels from air into water.
4. He strives after to run at least four fifths of the total route.
5. He takes another route.

 

[ separator ]


A rubber balloon is filled with air, made heavier by a mass hung from it by a string, and then submerged into the water of a swimming pool. With the upper side of the balloon just touching the surface of the water, the balloon remains to be suspended in the water.
What will happen if the balloon is pulled down to a depth of a meter and then let loose? Will it rise back to the surface of the water, will it sink to the bottom of the pool, or will it stay at the same depth?

 

[ separator ]


A ship is leaving the main port of Rotterdam, heading for the high seas.
As the ship navigates from the fresh water to the salt water, will the ship rise with regard to the surface of the surrounding water?
Will the ship rise with respect to a fixed landmark?

 

[ separator ]


When an accelerating aircraft approaches the speed of sound, it is going to break the sound barrier. Subsonic speed will be exchanged for supersonic speed and a loud sonic boom will be heard.
Is the sonic boom produced only at the moment an aircraft is passing through the sound barrier, or is it produced as long as an aircraft is travelling at supersonic speeds?

 

[ separator ]


Is a plummet really pointing exactly to the earth's centre of mass?
If not, are our buildings still standing perpendicular to the ground, supposing they are not out of lead?

 

[ separator ]


Twelve resistors, having a resistance of 30 Ω each, are connected agreeably to the twelve edges of a cube. A battery is connected to two opposite angular points of the cubic circuit.
What is the current in the battery if the potential difference between the two angular points is 1,5 V?

[ resistor cube ]

 

[ separator ]


A pure liquid, say substance A, has a density of 1250 kg/m. The density of another pure liquid (substance B) amounts 1000 kg/m at the same temperature.
After mixing different quantities of both liquids, the density of the obtained solution is 1150 kg/m at the same temperature as well. It is evident no contraction of volume has occurred.
What mass percentage of substance A is found in the mixture? (If your answer is less than 65,0 %, just try another way of thinking.)

 

[ separator ]


The animation shows the moon revolving about the earth with a period of just a few seconds instead of four weeks (27,3 or 29,5 days). Moreover, the real rotational period of the earth is 24 hours.

[ earth moon system ]

Give at least three more major differences between this model and the reality.

 

[ separator ]


Sometimes it's heard the moon is not rotating about its axis. Actually, it does. It is rotating at such a small rate that it is continuously facing the earth with the same side (*).
Is this behaviour purely a coincidence? Or can you contrive a more satisfying explanation?
(*) That's approximately true: the moon's orbit is slightly elliptical (5%) and slightly tilted (5°); hence we view each month's full moon from a slightly different distance and angle.

[ the moon ]

 

[ separator ]


Will the moon persist in not turning its back upon mother earth? If so, what stabilizing mechanism is behind it?

 

[ separator ]


A bar magnet is let loose at the top inside a vertical copper tube. Simultaneously, an identical magnet is let loose at the top inside a vertical plastic tube. The same holds with regard to an identical magnet in a vertical iron tube. The three tubes have the same geometrical dimensions.
In which order of succession will the falling magnets arrive at the bottom of the tubes?

 

[ separator ]


Can you create four equilateral triangles with sides at the length of one match, if you've got only six of them?

 

[ separator ]


When an air-liner or a military airplane takes off, you may happen to observe some accompanying mists over the wings of the aircraft.
How do these cloudlet-like mists originate?

[ a space shuttle (touching down) ] [ a Concorde ]

...even over the cockpit...   (a space shuttle is touching down; at the right a Concorde)
 

[ 1,1 Mach? ]

The same phenomenon, created in a slightly different way.

 

[ separator ]


What is the concentration of silver ions in a saturated solution at 25 °C prepared by dissolving silver carbonate in pure water? Shouldn't it have to be (358 ± 6) μmol/L rather than (255 ± 3) μmol/L?

 

[ separator ]


A heavy bullet made of steel is let loose at the centre of the ceiling in an empty lift-shaft of a very tall sky-scraper. In which geographical direction, viewed from the centre of the floor of the shaft, will it dash down?

[ lift-shaft ]

 

[ separator ]


A small wooden boat floats in a swimming pool. The level of the water at the edge of the pool is marked. The boat holds an iron anchor.
Will the level of the water rise, fall, or stay the same, if the anchor is removed from the boat and dropped in the pool?

 

[ separator ]


An ice cube floats in a glass of water filled to the brim. As the ice melts, will the glass overflow?
A similar ice cube floats in a glass of salt water filled to the brim. Will the glass overflow, while the ice melts?

 

[ separator ]


A long vertical tube is filled with water. A tiny balloon is filled with air and a mass of lead is tyed on it. After submerging the whole into the water, it remains suspended.
Will the balloon stay at the same depth, will it sink to the base of the tube, or will it rise to the surface of the water, when the temperature in the tube drops?
Is the way in which the system is cooling down affecting your answer? Does the cooling speed have any influence?

 

Hein ten Horn
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