Technical Problem Solving

Technical Problem Solving was a Division C event for the 2015 season. The event involves the gathering and processing of data to solve problems. The focus for the 2015 season was Forensic patterns of physical, not chemical, evidence associated with a crime scene.

Teams are allowed to bring any calculator and two double sided pages of notes, and are required to bring goggles. Supervisors will provide a more advanced calculator if necessary for a lab station. The event consists of two lab stations and up to 10 questions per station". The use of calculators and probes by supervisors is encouraged.

2015 Topics
Both topics will focus on Forensic patterns of physical not chemical evidence associated with a crime scene. Teams conduct experiments to solve crimes based on physical evidence.

Probes that may be used at the competition include temperature, dual force, motion detector, and colorimeter probes.

Topics in this year include Beer's Law, Newton's Law of Cooling, Random Error, Systematic Error, Regressions, Line of Best Fit, Standard Deviation, Normal Distribution, Residuals, Linear/Non-linear Transformation, and Extrapolation/Interpolation.

Beer’s Law
Beer's law also involves calculations to actually figure out the concentration of a solution from the absorbance measurements made by using the colorimeter (or spectrophotometer). There are three methods that can be used depending on what information is available. They involve using proportionality, graphing and Beer's Law.

1. The proportionality approach to these kinds of problems focuses on the idea that the absorbance of a solution is directly proportional to its concentration. When using this approach it is necessary to be sure that the values given are for different concentrations of the same chemical measured under the SAME conditions (BOTH wavelength and the path length).

2. The graphing method is called for when several sets of data involving STANDARD SOLUTIONS are available for concentration and absorbance. This is probably the most common way of Beer's law analysis based on experimental data collected in the laboratory.

Graphing the data allows you to check the assumption that Beer's Law is valid by looking for a straight-line relationship for the data.

3. You can directly use the Beer's Law Equation (Absorbance = e L c) when you are given the molar absorptivity constant (or molar extinction coefficient). In this equation, e is the molar extinction coefficient. L is the path length of the cell holder. c is the concentration of the solution.

Newton's Law of Cooling
Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings). Newton's Law makes a statement about an instantaneous rate of change of the temperature. We will see that when we translate this verbal statement into a differential equation, we arrive at the differential equation:


 * [math]\frac{\mathrm{d}T}{\mathrm{d}t}\propto T-T_a\Rightarrow \frac{\mathrm{d}T}{\mathrm{d}t} = k(T-T_a)[/math]

The solution to this equation is temperature as a function of time:


 * [math]T(t)=T_a + (T_0 - T_a)\mathrm{e}^{-kt}[/math]


 * [math]T_0[/math] is the temperature at time 0
 * [math]T_a [/math] is the ambient temperature
 * [math]k[/math] is some constant

Newton's Law would enable us to solve the following problem:
 * A person is found dead at noon and their temperature is recorded to be 35ºC. The temperature of the room they were found in is a frigid 17ºC. Ten minutes later the body's temperature is 34ºC.  Assuming that the person's body temperature was normal (37ºC) at the time of death, determine the time of death to the nearest minute.

Let [math]t=0[/math] represent noon, and let the unit of time be a minute.

Then, [math]T(10)=34=17+(35-17)\mathrm{e}^{-10k}[/math]

[math]17=18\mathrm{e}^{-10k}[/math]

[math]\frac{17}{18}=\mathrm{e}^{-10k}[/math]

[math]\ln\frac{17}{18}=-10k[/math]

[math]k=\frac{\ln\frac{18}{17}}{10}\approx 0.0057[/math]

Now, [math]T(t_{death})=37=17+18\mathrm{e}^{-0.0057t_{death}}[/math]

[math]\ln\frac{20}{18}=-0.0057t_{death}[/math]

[math]t_{death}=10\cdot\frac{\ln20-\ln18}{\ln17-\ln18}\approx-18.4[/math]

So the person died 18.4 minutes before noon, 11:42 AM.

Random and Systematic Error
Random error is caused by unknown/unpredictable changes (such as equipment/environmental). It limits precision.

Systematic error is in experimental observations, from error with instrument/operator. Examples include the zero setting error (when instrument is not showing zero when it’s measured zero), and the multiplier or scale factor error (when instrument consistently reads values greater/less than actual). It limits accuracy.

Past Topics
The general focus of TPS changes from year to year. Here are some topics it has covered in the past.

{|
 * 2014
 * 2014

2014
The topics for 2014 were electrochemistry and thermodynamics. Similarly to 2013, 80% of the weight was given to the lab itself, and 20% to the questions relating to the lab.

Electrochemistry
Electrochemistry is the study of chemical reactions involving the use of an electrical current. Events may use voltage, amp, and temperature probes.

Thermodynamics
Thermodynamics is the science related to thermal energy and its relation to matter. All levels of the competition will use a temperature probe. More in-depth information can be found here: Thermodynamics.
 * }

{|
 * 2013
 * 2013

2013
In 2013, the topics are more clearly defined than they have been in the past. This year will consist of two labs, one dealing with harmonics and sound, and the other regarding enzymatic reactions. The placement will be based off of how accurate teams' lab procedures and results are and their responses to questions related to the labs. 80% of the weight will be given to the accuracy of the answer from the lab, and 20% of the weight will be given to the test questions that relate to the lab.

Harmonics
The topic for Harmonics is the same for regionals, states, and nationals. All of them use a microphone as a probe and deal with open and closed tubes and strings.

Enzymes
This section studies the mechanisms governing enzymatic reactions using yeast catalase. As you advance through competition, additional topics are added:


 * Decomposition Rates (Regional)
 * Reaction Types (State)
 * Animal Catalase, Ideal Gas Law (National)
 * }

{|
 * 2012
 * 2012

2012
There are certain topics listed in the rules as the foci of this event:
 * Colorimetry
 * Temperature
 * CBR2 motion detector.

Colorimetry
Colorimetry is a chemical analysis procedure in which the absorption of a certain colored solution corresponds with its concentration.

Temperature
The use of temperature in this event is usually in analyzing colligative properties of solutions, and how they relate to temperature. Some of these properties include elevation of boiling point, freezing point depression, and lowering of vapor pressure.

CBR2 Motion Detector
A CBR2 motion detector is used for finding data related to motion, such as position, velocity, and acceleration. It measures motion using sound waves, and can plot points of position on a computer interface. They may be used in this event as a way for participants to analyze motion and the forces that govern it.
 * }

{|
 * 2010
 * 2010

2010
At the 2010 Cypress Falls Invitational in Texas, all problems involved measurement and basic formulae, such as area of a prism.

The 2010 national tournament featured various stations including calculating the periods of pendulums, measuring the volume of a 5-pointed foam star, measuring the volume of a block of wood with a hole drilled out of it, and calculating the acceleration of a ball bearing.
 * }

{|
 * 2009
 * 2009

2009
At the 2009 Los Angeles Regional competition, all problems were physics-based and very difficult. Calculus and extensive knowledge of formulae were both required. True to the event's name, problem-solving ability was vital. One of the problems was a proof-type problem.
 * }

Tips for Success in Technical Problem Solving

 * Practice is vital for this event. Make tests for one another, and remember imagination and creativity is a great asset for one to have on these tests!
 * Check out the test exchange for practice tests.
 * Keep calm and think carefully. Don't panic if you don't know how to solve a problem right away.  A few minutes of thinking can lead to key breakthroughs.
 * Keep track of time. Often, the station-based nature of the event will lead to tight time constraints.
 * Pay close attention to significant figures. Don't let yourself lose half a point per problem on account of incorrect sig figs.
 * Show all work, including elementary algebraic steps. Let there be no room for confusion in grading.
 * Know all physics formulae by heart. The equations used by the College Board for Advanced Placement Physics are a good place to start.  The event supervisor may or may not provide these formulae on the exam.
 * Stay organized and neat. The grading of this event is often very subjective, so it's important to make your test paper easy for the event supervisor to grade.

Links

 * Example Harmonics Lab
 * Example Enzyme Lab