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THE RULES :
1. Each person may attempt only one teaser, total, unless I announce otherwise.
2. If teasers remain unsolved after a significant length of time ( a couple of days), I will announce a 'free for all', at which time anyone (including those that have already answered) may attempt any number of the remaining questions.
3. Anyone may attempt the bonus question, even if they have already tried another question.
Note :
1. Some of these teasers require back-of-envelope type calculations, or 'order of magnitude' estimates.
2. All teasers are roughly aimed at the college/grad level. Some are accessible to high schoolers.
3. Please read the rules above and follow them.
THE TEASERS :
1. When liquid nitrogen or dry ice evaporates/sublimes, you can see thick, white fumes. If nitrogen and carbon dioxide are really white gases, why is air colorless ?
2. A planet forms from a large, cold cloud of dust. Neglecting radiation, find the radius of the planet (order of mag.) if its temperature keeps the planetary material at about its melting point.
Show working/explanation.
3. Experimental particle physicists have elaborate experiments set up (some, deep down in modified mine shafts) to observe proton decay. Derive a lower limit (very rough number) on the lifetime of the proton on the based on the fact that you are alive.
Assume that a dosage of about 600 rad is lethal. Also assume that a proton always decays into a positron and a neutral pion. Use Google for decay info or for conversions.
4. Sound can not propagate through vacuum.
In a popular demonstration of this, an electric bell is set up inside a bell-jar, which is then evacuated using a vacuum pump. When the air pressure drops below about 1cm of Hg, the bell is no longer audible. Voila !
Show why this demonstration is spurious, and, if you can, provide the correct interpretation.
5. BONUS QUESTION :
Resolve this paradox.
The Earth is not a sphere, but is, approximately, an oblate spheroid, with its equatorial diameter a about 13 miles (21 km) greater than its polar diameter b. Modeling this in 2 dimensions, as an ellipse, you have x = a~cos \theta, ~~y=b~sin \theta. Writing a-b=\delta and neglecting squares of \delta /a, the equation yields r = \sqrt{x^2 + y^2} = a - \delta sin^2 \theta, where \theta is the latitude. This gives r_{30} - r_{50} = 4.6~mi (about 7.4 km). So a point on the sea level at a latitude of 30N is about 4.6 miles higher than a similar point at 50N.
Now the Mississippi River flows from roughly 50N to about 30N, where it drains into the Gulf of Mexico. The altitude at the source is about 1.5 miles above mean sea-level, and the mouth is obviously at sea-level. Now, what this means is that the river has effectively climbed a height of about 3 miles in its journey to the sea.
But we all know that water can not flow upwards against gravity, from a smaller height to a greater one. So the Mississippi is a figment of our imagination.
That's all for now...more coming up after this.
1. Each person may attempt only one teaser, total, unless I announce otherwise.
2. If teasers remain unsolved after a significant length of time ( a couple of days), I will announce a 'free for all', at which time anyone (including those that have already answered) may attempt any number of the remaining questions.
3. Anyone may attempt the bonus question, even if they have already tried another question.
Note :
1. Some of these teasers require back-of-envelope type calculations, or 'order of magnitude' estimates.
2. All teasers are roughly aimed at the college/grad level. Some are accessible to high schoolers.
3. Please read the rules above and follow them.
THE TEASERS :
1. When liquid nitrogen or dry ice evaporates/sublimes, you can see thick, white fumes. If nitrogen and carbon dioxide are really white gases, why is air colorless ?
2. A planet forms from a large, cold cloud of dust. Neglecting radiation, find the radius of the planet (order of mag.) if its temperature keeps the planetary material at about its melting point.
Show working/explanation.
3. Experimental particle physicists have elaborate experiments set up (some, deep down in modified mine shafts) to observe proton decay. Derive a lower limit (very rough number) on the lifetime of the proton on the based on the fact that you are alive.
Assume that a dosage of about 600 rad is lethal. Also assume that a proton always decays into a positron and a neutral pion. Use Google for decay info or for conversions.
4. Sound can not propagate through vacuum.
In a popular demonstration of this, an electric bell is set up inside a bell-jar, which is then evacuated using a vacuum pump. When the air pressure drops below about 1cm of Hg, the bell is no longer audible. Voila !
Show why this demonstration is spurious, and, if you can, provide the correct interpretation.
5. BONUS QUESTION :
Resolve this paradox.
The Earth is not a sphere, but is, approximately, an oblate spheroid, with its equatorial diameter a about 13 miles (21 km) greater than its polar diameter b. Modeling this in 2 dimensions, as an ellipse, you have x = a~cos \theta, ~~y=b~sin \theta. Writing a-b=\delta and neglecting squares of \delta /a, the equation yields r = \sqrt{x^2 + y^2} = a - \delta sin^2 \theta, where \theta is the latitude. This gives r_{30} - r_{50} = 4.6~mi (about 7.4 km). So a point on the sea level at a latitude of 30N is about 4.6 miles higher than a similar point at 50N.
Now the Mississippi River flows from roughly 50N to about 30N, where it drains into the Gulf of Mexico. The altitude at the source is about 1.5 miles above mean sea-level, and the mouth is obviously at sea-level. Now, what this means is that the river has effectively climbed a height of about 3 miles in its journey to the sea.
But we all know that water can not flow upwards against gravity, from a smaller height to a greater one. So the Mississippi is a figment of our imagination.
That's all for now...more coming up after this.
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i have actually never seen it...