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Pool-shark billiards

September 10, 2014| Papers Haven

Extra credit questions (to be submitted by Monday June 2nd at lecture and printed out on paper; no handwritten submissions will be accepted.)

1.    Do you remember my demonstration of radiative transfer of thermal energy? I shone a beam of light from a lamp onto a “weathervane-like” contraption and instantly, the vanes began revolving as if by magic. I explained that the hot lamp had sent waves of energy to the vanes penetrating through the vacuum in the bulb where the vanes were housed. It was this radiative energy that caused the conditions for the vanes to move. I should also have stated that all objects send out radiative energy and that if I had placed the contraption in bright sunlight the vanes would have moved too. The natural question then arises as to why the lamp and the sun can achieve that but that we who are also emitting radiative energy cannot. For a half (1/2) course point, give me the answer to that question with a full explanation.

2.    Explain through physical concepts why the following are “words of wisdom”:

When you are making a hardboiled egg, turning up the heat after the water comes to a boil does not hasten the process. (1/4 course point)

Blow with a wide open mouth and then with your lips only slightly parted. The first feels hot, the other cold. (1/4 course point)

3. You and a friend are watching a pool-shark showing off his prowess at billiards. In one demonstration, the pool-shark placed two billiard balls, one red and the other white, near each other on the table, then fires off the red ball so that it strikes one side of the table (A), then an adjacent second side (B), followed by the next adjacent third side (C) before colliding with the white ball. Your friend says she knows how she can do the same trick, at least in theory. She picks up a piece of paper, and then sketches a rectangle to represent the billiard table. She asks you to insert two small circles to represent the balls anywhere on the table. Taking the paper back from you and using a pencil and a ruler, she then draws the “complete trajectory of the red ball” as she would launch it so as to repeat the pool-shark’s feat. If the drawing below is what you handed your friend, can you repeat what she did and show the trajectory she drew? (You must be as accurate as you can be to receive any points at all. A good guess gets you nothing. There is only one “path” that is allowable to your friend. Your drawing must clearly illustrate how she found it and explain the process in words as well.) (1/2 course point)

Having learned the “secret” behind how to solve this problem, show as many ways as you can that will allow you to fire the red ball so as to have it collide with the white ball after hitting four sides of the table (the red ball can hit any given side only once and in any order). (1/2 course point)

Hint: Your friend used a concept in physics not related to mechanics to “solve” the problem, the law of reflection. Go to this website (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=41.0) and play the billiards “game” to get an idea for the solution.  Note that in our problem there are no pockets where the balls will be “captured”.

D                                   C                                                  B                                             A
Extra credit questions (to be submitted by Monday June 2nd at lecture and printed out on paper; no handwritten submissions will be accepted.)

1.    Do you remember my demonstration of radiative transfer of thermal energy? I shone a beam of light from a lamp onto a “weathervane-like” contraption and instantly, the vanes began revolving as if by magic. I explained that the hot lamp had sent waves of energy to the vanes penetrating through the vacuum in the bulb where the vanes were housed. It was this radiative energy that caused the conditions for the vanes to move. I should also have stated that all objects send out radiative energy and that if I had placed the contraption in bright sunlight the vanes would have moved too. The natural question then arises as to why the lamp and the sun can achieve that but that we who are also emitting radiative energy cannot. For a half (1/2) course point, give me the answer to that question with a full explanation.

2.    Explain through physical concepts why the following are “words of wisdom”:

When you are making a hardboiled egg, turning up the heat after the water comes to a boil does not hasten the process. (1/4 course point)

Blow with a wide open mouth and then with your lips only slightly parted. The first feels hot, the other cold. (1/4 course point)

3. You and a friend are watching a pool-shark showing off his prowess at billiards. In one demonstration, the pool-shark placed two billiard balls, one red and the other white, near each other on the table, then fires off the red ball so that it strikes one side of the table (A), then an adjacent second side (B), followed by the next adjacent third side (C) before colliding with the white ball. Your friend says she knows how she can do the same trick, at least in theory. She picks up a piece of paper, and then sketches a rectangle to represent the billiard table. She asks you to insert two small circles to represent the balls anywhere on the table. Taking the paper back from you and using a pencil and a ruler, she then draws the “complete trajectory of the red ball” as she would launch it so as to repeat the pool-shark’s feat. If the drawing below is what you handed your friend, can you repeat what she did and show the trajectory she drew? (You must be as accurate as you can be to receive any points at all. A good guess gets you nothing. There is only one “path” that is allowable to your friend. Your drawing must clearly illustrate how she found it and explain the process in words as well.) (1/2 course point)

Having learned the “secret” behind how to solve this problem, show as many ways as you can that will allow you to fire the red ball so as to have it collide with the white ball after hitting four sides of the table (the red ball can hit any given side only once and in any order). (1/2 course point)

Hint: Your friend used a concept in physics not related to mechanics to “solve” the problem, the law of reflection. Go to this website (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=41.0) and play the billiards “game” to get an idea for the solution.  Note that in our problem there are no pockets where the balls will be “captured”.

D                                   C                                                  B                                             A

 Answer

 

  1. Do you remember my demonstration of radiative transfer of thermal energy? I shone a beam of light from a lamp onto a “weathervane-like” contraption and instantly, the vanes began revolving as if by magic. I explained that the hot lamp had sent waves of energy to the vanes penetrating through the vacuum in the bulb where the vanes were housed. It was this radiative energy that caused the conditions for the vanes to move. I should also have stated that all objects send out radiative energy and that if I had placed the contraption in bright sunlight the vanes would have moved too. The natural question then arises as to why the lamp and the sun can achieve that but that we who are also emitting radiative energy cannot. For a half (1/2) course point, give me the answer to that question with a full explanation.

Human beings emit energy in the form of infra-red rays while the sun and the lamp emit heat inform of UV rays which have a shorter wavelength. Infrared rays have longer wavelengths and this reduces their energy making it harder for them to move the vanes. The frequency is not high enough to cause the conditions for the vane to move. In addition, we are always wearing insulating layers, clothing which keeps in some of my…

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