Cell phones periodically need to be recharged. However, many people always keep their recharger plugged in. Additionally, many people charge their phones every night, whether they need to be recharged or not. Model the
energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2. Assume that the Pseudo US supplies electricity from oil. Interpret your results in terms of barrels of oil. Requirement 4
Estimates vary on the amount of energy that is used by various recharger types (TV, DVR, computer peripherals, and so forth) when left plugged in but not charging the device. Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day. Requirement 5
Now consider population and economic growth over the next 50 years. How might a typical Pseudo US grow? For each 10 years for the next 50 years,
predict the energy needs for providing phone service based upon your analysis in the first three requirements. Again, assume electricity is provided from oil. Interpret your predictions in term of barrels of oil.
2010MCM
PROBLEM A: The Sweet Spot
Explain the ―sweet spot‖ on a baseball bat.
Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power
is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple
explanation based on torque might seem to identify the end of the bat as the sweet spot, but
this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.
Some players believe that ―corking‖ a bat (hollowing out a cylinder in the head of the bat and
filling it with cork or rubber, then replacing a wood cap) enhances the ―sweet spot‖ effect.
Augment your model to confirm or deny this effect. Does this explain why Major League
Baseball prohibits ―corking‖?
Does the material out of which the bat is constructed matter? That is, does this model predict
different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major
League Baseball prohibits metal bats?
PROBLEM B: Criminology
In 1981 Peter Sutcliffe was convicted of thirteen murders and subjecting a number of other people to vicious attacks. One of the methods used to narrow the search for Mr. Sutcliffe was to find a ―center of mass‖ of the locations of the attacks. In the end, the suspect happened to live in the same town
predicted by this technique. Since that time, a number of more sophisticated techniques have been developed to determine the ―geographical profile‖ of a suspected serial criminal based on the locations of the crimes.
Your team has been asked by a local police agency to develop a method to aid in their investigations of serial criminals. The approach that you develop should make use of at least two different schemes to generate a geographical profile. You should develop a technique to combine the results of the different schemes and generate a useful prediction for law enforcement officers. The prediction should provide some kind of estimate or guidance about possible locations of the next crime based on the time and locations of the past crime scenes. If you make use of any other evidence in your estimate, you must
provide specific details about how you incorporate the extra information. Your method should also provide some kind of estimate about how reliable the estimate will be in a given situation, including appropriate warnings.
In addition to the required one-page summary, your report should include an additional two-page executive summary. The executive summary should
provide a broad overview of the potential issues. It should provide an overview of your approach and describe situations when it is an appropriate tool and situations in which it is not an appropriate tool. The executive summary will be read by a chief of police and should include technical details appropriate to the intended audience.
2011MCM
PROBLEM A: Snowboard Course
Determine the shape of a snowboard course (currently known as a ―halfpipe‖) to maximize the production of ―vertical air‖ by a skilled snowboarder.
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Tailor the shape to optimize other possible requirements, such as maximum twist in the air.
What tradeoffs may be required to develop a ―practical‖ course?
PROBLEM B: Repeater Coordination
The VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by ―repeaters,‖ which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.
In addition to geographical separation, the ―continuous tone-coded squelch system‖ (CTCSS), sometimes nicknamed ―private line‖ (PL), technology can be used to mitigate interference problems. This system associates to each
repeater a separate subaudible tone that is transmitted by all users who wish to communicate through that repeater. The repeater responds only to received signals with its specific PL tone. With this system, two nearby repeaters can share the same frequency pair (for receive and transmit); so more repeaters (and hence more users) can be accommodated in a particular area.
For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter
frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available.
How does your solution change if there are 10,000 users?
Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.