Ruppert 1
Nicklaus Karl Ruppert
Math 7
Peter Winkler
5/15/13
Physics as the Answer to “Why?”
Physics, and all the concepts surrounding it, revolve around the question,
“Why?” Why do things happen the way they do? What causes them to happen?
Physics can explain most natural phenomena that occur in our world today. These
explanations came about through events of discovery, loss, disagreement, and
rediscovery (Feimer). Today, most questions can be answered through observations
made from those previous events. In some sense, each question about a natural
occurring phenomenon appears as a puzzle. These puzzles question either, “Why
would this happen?” or What would happen if…?” Physics puzzles involve natural
occurrences in which the puzzle may only be solved through investigation about
why things happen the way they do. Though this may sound quite simple and
straightforward, answering the question “why?” has been quite a process of complex
discovery.
Physics has been around for as far back as history dates. The wheel goes far
back enough that the archeologists have to estimate when it may have been
invented. At some point, humans must have figured that a circle rolls more
efficiently than any other shape, and therefor became the method of transportation
for objects man couldn’t carry on their own. This occurred through observation and
discovery. As the wheel developed over time, so did nuances that made
transportation even more efficient. Instead of having to replace each roller as an
object advanced, axles where invented to keep the rollers constant. Rubber wheels
*All problems and proofs are from Gardner, Martin
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and a solid core reduced wear and tear because they have stronger characteristics
than wood or spokes for example (Invention, 1). Why would we want to use these
materials? Physics explains this through proof of increase in efficiency. As more
discoveries have been made, human action has become more efficient. Humans have
always wanted to know more, which explains why we’ve developed the evergrowing knowledge we have today (Feimer).
Some of the most famous names of all time were Galileo Galilei and Isaac
Newton. These are two of countless names of people to make great discoveries in
physics, but provide excellent examples in how to approach physics. Both carried
constant curiosity and passion in understanding the world. Where Aristotle thought
larger objects fall faster than smaller ones, Galileo delved deeper into the subject,
and discovered forces such as friction and gravity. These helped determine how fast
an object would fall, or move. In addition to these discoveries, further observation
and discovery was made with Isaac Newton. He discovered how two forces act on
one another. For example, pushing a box would cause the box to move forward, but
would change the shape of one’s hand (flatten and expand) as force is being applied
on both objects. He also found that the force on an object depends on its rate and
acceleration (F=ma)(History). Discoveries about the world continue today, in even
more complex and diverse fashions. The curiosity surrounding the field of physics
drives human’s increase in knowledge.
The approach on physics questions must be intelligent and thought out.
When presented with a question or problem, we must take approaches similar to
those who’ve made great discoveries, such as Galileo and Newton. With an earnest
*All problems and proofs are from Gardner, Martin
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curiosity and passion to prove or discover an answer, one gives themselves the
opportunity to reach a solution. Galileo and Newton certainly didn’t just come about
their great discoveries. They spent their lives questioning and discovering
occurrences. We too can answer why things occur, so long as the right effort is
exerted.
With examples from Martin Gardner’s The Colossal Book of Short Puzzles and
Problems, we can explain an approach in answering “why?” that makes sense and
provides real life solution to natural occurring events. First, one must read a
question thoroughly, as mistakes can be easily made. Once one has an
understanding for the situation, the unknown can be defined. In physics, the
unknown may be the reason something ends up the way it does, or the actual ending
to causation. In problem 17.4, the solver is presented with a situation in which a
cardboard horseshoe and a toothpick are leaning against each other as such:
The problem asks the solver how to lift the horseshoe by means of only a
second toothpick. The toothpick may not be split in half and used like chopsticks,
and only the toothpick may come in contact with the other toothpick and horseshoe.
*All problems and proofs are from Gardner, Martin
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How is it done? In this case, the unknown happens to be the ending to the causation.
The unknown is suspending the horseshoe and toothpick in the air with only
another toothpick. In G. Polya’s How to Solve It, he address the unknown as, “the
corresponding Latin saying is: “respice finem.” That is, look at the end. Remember
your aim. Don’t forget your goal. Think of what you are desiring to obtain. Do not
lose sight of what is required. Keep in mind what you are looking for” (Polya 123).
This may be old, generic advice, but concentrating on this may allow the solver to
envision what the solution is. In this case, envisioning the goal can lead the solver to
figure that the only possible way to keep both objects suspended by a toothpick
would be to balance either object. If the solver maneuvers the leaning toothpick
carefully under the curved part of the horseshoe and finds a balance point, both
objects may be raised in the air and suspended as such:
After defining the unknown, a plan must be devised. The solver must ask how
to solve the problem, using sound logic and accurate physics. In problem 17.15, a
family is driving in a car, with all the windows and vents shut tight. A child holds a
string attached to a helium filled balloon that floats just below the car’s roof. The
question asks what will happen (which direction will the balloon float towards)
*All problems and proofs are from Gardner, Martin
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when the car accelerates or turns around a curve. In devising a plan, Polya address
that, “we know, at least in outline, which calculations, computations, or
constructions we have to perform in order to obtain the unknown” (Polya 8). In this
case, one must draw up the situation, and acknowledge the characteristics of the
elements involved. Since helium is lighter than normal air (why helium balloons
float) the balloon would slide forward when accelerating since the normal air would
be pushed back by inertia, and force the lighter helium forward in its place. The
same applies to a curve, in which the balloon would slide into the curve. The plan in
solving this puzzle may simply be tested in real life as well, and proven.
Every factor involved plays a role in physics. None may be overlooked, or the
correct solution may never be found. Polya states that, “if the proof neglects any part
of the hypothesis, the proof must be wrong” (Polya 96). In problem 17.14, a small
boy is sailing a plastic boat, filled with nuts and bolts, in a bathtub. If the boy dumps
all the cargo in the water, leaving the boat to float empty, will the water level rise or
fall? In this case, the data given says the nuts and bolts float in the ship, in which
they displace the amount of water equal to their weight. When sunk in the water,
they now displace the amount of water equal to their volume. The proof states that
since the pieces weigh more than the volume of water they’re displacing, the water
level will lower. Notice that this proof addresses every factor: the nuts and bolts
weight and volume, and the water’s weight and volume. The proof holds validity.
In every case of a physics problem or puzzle, the solver has to take an
intelligent approach. Polya addresses an intelligent problem-solver as, “he connot
attain real understanding unless he comes across the procedure that the question
*All problems and proofs are from Gardner, Martin
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tries to provoke in his own work and, by having experienced its usefulness,
discovers the proper use of the question for himself” (Polya 206). Problem 17.1
presents a case where a truck driver with an air-tight trailer full of 200 pigeons is
about to cross a sketchy bridge. He wants to lighten his load so he bangs on the side
of the trailer to provoke the birds to fly around and therefore “lighten” the load. Can
anything be said of his reasoning? For solving this problem intelligently, one must
do some research, which much of physics revolves around. When the pigeons are at
rest in the trailer, the weight remains constant, as simply inferred. After various
investigations, the solver may find that with every flap of a bird’s wing, an upward
and downward force from acceleration will be exerted. As the birds flap up, the
weight of the trailer will decrease. As the birds flap down, the weight of the trailer
will increase. Constant fluctuation of weight will result. However, this fluctuation of
weight will run just above and below the weight when the pigeons are at rest. This
fluctuation results as about the same weight of the trailer with the birds at rest.
Therefore, the truck driver’s theory holds invalid. With the right questioning and
investigation, the solver may find the correct solution here.
A lasting characteristic of physics is that the field has no grey areas.
Questions and proofs appear as straightforward as possible, since physics deals with
factual episodes. No underlying meaning can explain how something occurs. Natural
events occur because something definitely happened. So, in explaining a problem
involving physics, writing a concise proof to answer why something happens must
have concision. Problem 17.3 presents an iron doughnut. When the iron doughnut
heats up, will the diameter of the hole get wider or smaller? If tested, the solver will
*All problems and proofs are from Gardner, Martin
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find that the iron doughnut will expand with heat. Yet, as the iron expands, it will
keep its same proportions. Therefor, the diameter will get larger. In writing this
proof, one must clearly explain how iron expands with heat, and that in doing so, the
proportions will stay the same. As Gardner does, a real life event may provide
excellent evidence as well. In his proof, he explains that optometrists heat eyeglass
lenses in order to release the lens from the frame. The frame expands, keeping its
proportions, yet frees the glass from its grip. In this state, his proof appears as
concise as possible.
To confirm any results validity, if ever unsure, checking it with real life
application is also an option, since physics involves real life application after all. In
problem 17.5, the problem addresses a phenomenon in which a cork is placed in the
center of a glass of water. The cork will always float to the edge of the glass. The
problem asks how to make the cork stay in the middle of the water, not touching the
glass. Nothing may be in the glass but water and the cork. Why does the cork always
float to the side? At any time while the water level is below the brim of the glass, the
water will form to the sides of the glass in a concave shape (called meniscus). Since
the cork floats, it will sit at the highest point of water level, which is at the edge of
the meniscus. If one were to fill the glass just above the brim of the glass, the shape
of the meniscus would change to a convex shape, in which the middle of the water
would be the highest point and the cork would stay in the center. This can be very
easily proven through experiment, and explained quite concisely as well. All one
really needs to understand is the shape of the meniscus below and above the brim of
the glass. One can see these shapes with actual application.
*All problems and proofs are from Gardner, Martin
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Why all these proofs hold validity develops in natural proof and explanation.
Reaching this destination involves six important approaches: Define the unknown.
Devise a plan. Use all the data. Take an intelligent approach. Write a concise proof.
Check the result. These approaches can guide one to what they would like to prove,
but what one proves must occur naturally. In solving, previous knowledge and new
investigation ought to transpire. Research as to what certain things can and can’t do
lead the solver down the path toward solution.
The solution states or proves why things happen the way they do, because of
physics. Curiosity such as that of Galileo and Newton will drive ones search to find
more, or discover new efficiency such as that of the wheel. Physics, and its lasting
state, can and will explain what is and why. The solver just needs to examine with
energy.
*All problems and proofs are from Gardner, Martin
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Works Cited
Feimer. "History of Physics." www.physicsphenomena.com. The American Institute
of Physics, n.d. Web. 21 May 2013. <http://www.physicsphenomena.com/
HistoryofPhysics.htm>.
Gardner, Martin. The Colossal Book of Short Puzzles and Problems. Ed. Dana
Richards. New York: W.W. Norton & Company, Inc., 2006. Print.
"Invention of the Wheel." library.thinkquest.org. Oracle Education Foundation,
n.d. Web. 21 May 2013. <http://library.thinkquest.org/C004203/science/
science02.htm>.
Polya, G. How to Solve It. Princeton: Princeton University Press, 1985. Print.
*All problems and proofs are from Gardner, Martin