unit 2
Data
Always Double-Check Your Data Could there be life on Mars? Is there oxygen in their atmosphere? At 6:45 pm on December 11, 1998, the unmanned Mars Climate Orbiter Spacecraft was launched from Cape Canaveral, Florida to study the Martian atmosphere. The spacecraft was mounted to a single-use Delta II rocket, where each launch costs 36 million dollars; the total cost of the mission was 125 million dollars. The fuel for the launch was a combination of kerosene and liquid oxygen for the main rocket, and four solid rocket boosters containing a fuel known as HTPB, which is similar to man-made rubber, with an approximate molecular formula of C3H4. Several other fuels are used during the one hour cruise into space, including solid rocket boosters to prevent spinning. The details of this mission are available in detail from the NASA website. 9 months later the spacecraft had completed the 48 million mile trip and began orbiting Mars. It passed behind Mars, where radio contact was lost, as expected. However, nothing was ever heard from the spacecraft again.
Above: The Mars Climate Orbiter Below: The Delta II Rocket
Findings of the failure review board indicate that a navigation error resulted from some spacecraft data being reported in Imperial units instead of metric. Oops. This bonehead error caused the spacecraft to miss its intended 140–150 km altitude above Mars during orbit insertion, instead entering the martian atmosphere at about 57 km. The spacecraft is believed to have been destroyed by atmospheric stresses and friction at this low altitude. Like the Mars Climate Orbiter, in this unit each of you will be given the opportunity to discover something new. The topic is the Mentos Eruption, where mentos candies are dropped into a soda bottle, and a fountain of soda erupts violently out of the bottle. One of the reasons this is such a wide open field for discovery, is that, to date, there is only one published scientific article on the topic. Ask any question you like about this phenomenon and try to get to the bottom of it. Be sure to double check your data.
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Introduction 2 Table of Contents 3 Lab 2.1: Mentos Eruption 4-8 Lecture 1.1: Data 9-14 Worksheets 15-20 Review 21-22
Which of these magazines embraces the peer-review system?
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You've probably seen or performed this famous experiment. Drop a few Mentos brand candies into a bottle of soda and watch it erupt. It's fun, and it makes you wonder about many things- how does it happen? Will other candies work? What is the record for height (29 feet)? This week we will be performing experiments designed by students to figure out what is going on with the mentos eruption. Before going any further, safety must be mentioned.
Experiments should only be performed in the classroomnever at home. Like many experiment, there are some very dangerous versions of this experiment that are posted on YouTube and other sites that must not be performed. The experiments in the classroom will be carefully monitored with a focus on safety. Having said that, this experiment is a great opportunity to perform real research. Prior to 2008, the only published scientific papers concerning this phenomenon were published in the two volumes of the Guilford Journal of Chemistry. Finally, in February 2008 a paper by Professor Tonya Coffey was published in the American Jounal of Physics. Titled Diet Coke and Mentos: What is really behind this physical reaction? A U.S. Patent was also recently awarded to Steve Spangler which includes background research into the eruption, and detailed schematics for bottle attachments. All students are required to read the Coffey Paper, and the summaries or full papers in the Guilford Journals of Chemistry.
The Mentos Eruption is a blast.
Most of what is written about the Mentos Eruption is unverified. Three sources of information that have been checked by others include two volumes of the Guilford Journal of Chemistry, and a paper by Professor Tonya Coffey. These are
required reading for all students. Click on the covers to learn more.
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Today you will be asked to choose your discovery topic for the mentos eruption. To help you choose your topic, several groundbreaking papers from previous years have been highlighted. Click on any paper to learn more.
Intro. to Volume 1
Required Reading
Intro. to Volume 2
Mint Heating
Warm Soda
Nozzles
Soda Type
Mint Type
Height Optimization
Soda Type
Nozzles
Required Reading Your goal is to discover something new about the Mentos eruption, and publish your results.
After you’ve completed reading these papers, here are some ideas for research projects: 1. Test the nucleation theory by coating mentos with something else, or creating mentos sized objects with different surfaces to see if it is all about these microscopic pits 2. Do a definitive study comparing soda types, mint types, nozzle sizes, temperature, volume, or time. 3. Supercool the mentos using dry ice…will it lead to a massively high eruption? 4. Add weights to the mentos to make therm drop at different rates 5. What would a scale measure during a mentos eruption if placed under the bottle? This could be a physical study. 6. Another force idea would be to create a spinning bottle, or a pendulum effect. 7. Coffey states that the key to the mentos reaction is a rough surface and a surfactant (a substance that lowers surface tension, like dishwashing liquid)…use this to make an artificial mento candy. 8. Skeptical of someone elses research? Repeat their work and publish a paper disproving it, modifying it, or discovering something else. 8. Use your imagination- many other exciting experiments are possible.
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Names:___________________________________________ and ___________________________________ (2 maximum)
Period:____
Mentos Lab Report: Working Title Most great discoveries begin with thorough research. Be sure to read the two volumes of the Guilford Journal of Chemistry, and the paper by Tonya Coffey. Come up with a useful experiment designed to discover something new about the Mentos Eruption. 1. Create a Working Title: One sentence that states what you plan to discover. Odds are the title will change, but it’s good for now. For example: “Wax-coated Mentos reliably delay a Mentos Eruption”, or “Nozzle size is Proportional to Mentos Eruption Height” are some good working titles. An excellent final title quantitatively states a significant new discovery.
Working Title:
2. List your planned experimental procedure.
2. Your list of things to bring in next class:
3, Obtain your stamp of approval from your instructor.
Stam-p of approval 6
Publication Guide All Students: Your results will be considered for publication in The Guilford Journal of Chemistry . Note that as for all scientific research, you must produce new and significant scientific results to be considered for publication in this journal. This is probably your first scientific publication. These are serious business, the work a scientist is most proud of. If well done, you can include them on your resume. They can help you get into college. Most importantly, they are the cutting edge of science: the new things that have just been discovered, by you. The bar is high: nothing can be simply stated without evidence, usually described using endnotes. If your work cannot be repeated by others it results not in progress, but in confusion. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Publication Guidelines: The typed Journal report is due on the date specified. There will be a 10% deduction for each late day. The format is that of a typed scientific journal research article. Use the most recent Journal to assist you. You will be graded on the content in 10 areas (scoring guide follows): 1. A Title that states what you discovered. 2. Your names. 3. A one paragraph summary of your experiment and results. For Level 1 and Honors students this includes a mathematical formula which summarizes your discovery. 4. An introduction that summarizes what is known in your research area, with endnoted references. Use quality references such as that in previous Journal volumes. Websites may NOT be used. See the reference section below for details. Be sure you have read the required reading article “Scientific Writing�. Note that great scientific discoveries can be made by anyone. For example, a local Arkansas kayaker spotted a bird (the ivory billed woodpecker) thought to be extinct in 2005 and published his paper in Science Magazine. Note the quality of the references in this paper. 5. An experimental section that briefly describes your experiment in a simple paragraph. If your experiment is design-based, (for example the design of a remote control system) each iteration can be described here. 6. A results section. This must include your data and a graph. SI units must be used. Scientific notation should be used when appropriate. 7. A conclusion section. For Level one and Honors students this must include a mathematical formula which summarizes your discovery quantitatively For all students this should include a discussion of the significance of the results, and suggested follow-up experiments. This is also a good place to assess the reliablility of your data. Be careful to be cautions in stating your conclusions, and support your conclusions with data. 8. An Experimental Procedure section. This describes your optimized procedures in a listed series of steps, and must be repeatable by a stranger. 9. A list of references should be the last section of your paper. This is a scientific research paper, and the information on which your research is based has to be verified. If you are doing this well, this will be the most time consuming section to produce. Each reference must be cited in the paper. Web sites may NOT be used. Consider using Google Scholar as a source for high-quality peer reviewed references. This is the hardest part. General websites such as Wikipedia may NOT be used. See the introduction to the journals for good exampls of the proper use of scientific references. Be sure you have read the article titled Scientific Writing; this is required reading for all students.
Report due: ______________ The best way to be sure your publication is awesome is to grade yourself using the scoring guide on the following page.
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After the discovery itself, the references are the most important part of your scientific paper. They are the foundation on which your work is based, and must be known to independently verified. This is the basis for the peer review systerm. All students are required to read the article “Scientific Writing�. Remember, anyone can make an important scientific discovery. Mentos Lab Report Scoring Rubric Read this to make sure you get a nice high score. Topic Value 1. Title (10 points) Is present States what you discovered 2. Summary (10 points) Is present Summarizes the results Uses numbers or percents to get quantitative results 3. Introduction (10 points) Is Present Includes relevant references Explains the Mentos eruption using only conclusions supported by verifiable experiments Is related to the experiment 4. Experimental Section (10 points) Is present Is repeatable by a stranger 5. Results (10 points) Are present with a graph Are described using numbers L1, Honors only: Results summarized with a mathematical formula. Do not contain suspect data 6. Conclusion Is present Cautiously discusses the significance of the results Tries to explain the reasons for the results Suggests relevant follow-up experiments 7. Endnotes Are included for any statement that needs support; minimum of 10. Are described as well as cited Do not contain websites. After a full citiation, they may be included for convenience to the reader Total
Your Score
Explanation
5 5 5 5 3 2 2 3 3 2 5 5 3 2 4 1 3 5 1 1 10 5 5
8 80
Units Fahrenheit, Celsius, or Kelvin‌for some reason people can’t seem to agree on common units. But we continue to try- in Europe the Euro is a good example. On this slide the seven most common units of measure that we are supposed to use are listed. Note how few of them are commonly used. Some units of measure such as density use two units at once- they are combined units. Practice problems are available in worksheet 2.1
Combined Unit Calculations Since density = mass/volume, if we know two of these measurements, we can calculate the third. Mastering this takes a little practice, so here are two solved examples. There are more problems of this type in worksheet 2.2.
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Prefixes These are those handy little modifiers that tell you how many, like a gigabyte (a billion bytes), or a kilometer (a thousand meters). Good stuff to know. See worksheet 2.1 for problems.
Temperature Fahrenheit, Celsius, or Kelvin…we in the USA prefer degrees Fahrenheit, while most of the rest of the world is more comfortable with degrees Celsius. Scientists, on the other hand, are aware that there are times when only Kelvin will do. Since it can never be negative, it is the only form of temperature which makes sense when performing calculations. To be on the safe side, methods are shown for interconverting all three common temperature units. See worksheet 2.2 for problems.
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Scientific Notation Scientists measure the very large and the very small, like the mass of the earth (5,974,200,000,000,000,000,000,000,00 0 grams, give or take) or the mass of an electron (0.000000000000000000000000000910 938188 grams) And writing all of those zero’s gets old fast. Scientific notation makes it a breeze‌once you get the hang of it. You can find additional problems in worksheet 2.3.
Scientific Notation: On your Calculator Or, how I learned to love my exponent button.
Most students enter scientific notation into their calculators by copying each number down, using parentheses always, and using the carat button (^) for exponents and the negative sign, not the minus sign, for negative numbers or exponents. That’s a mouthful. Well that works, but if you use your exponent button instead (it is either E, EXP, or EE depending on the calculator), it is far fewer keystrokes and no parentheses are needed,. For example 2E8 means 2 x 108. Easy.,
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Unit Conversions Most of us know that 24 eggs can be converted to 2 dozen eggs,; but converting 65 miles per house into meters per second is another matter. The way through this is to learn a foolproof method for the easy ones, then use it for harder ones, as these slides do. People perform unit conversions in their head all the time. To pass the time, I calculate my running pace in minutes per mile (min/mile) while I run. Follow the conversions on these slides, and then work on the additional problems in worksheet 2.4.
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Significant Figures A scientist measures the height of three mentos eruptions to be 2, 3 and 5 meters. How should he report the average height of the eruption? 3.3333 meters? That seems far too precise for such widely varying data. Questions like these can be at least partially answered using established rules for significant figures, which are guidelines for the level of precision to use when working with data. L2 students should know the level of precision to use when measuring: one digit beyond the markings or graduation in a device. L1 and honors students should also know how to mathematically apply these data. Problems are available in worksheet 2.5.
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Finding Formulas The precept known as Occam’s Razor states that in general the simplest answer tends to be the best one. Distilling an observation down to a mathematical formula is about as simple as it gets, and at the same time is one of the hardest scientific things to do. It demands rock-solid data. The formula may be difficult to work out. Two examples are shown in the slide on the left.. Problems are available in worksheet 2.5.
Percent Error Percent error reminds me of a grade on a test, only in this case, it is a bad thing to get better than a perfect cover. In the example given in the slide, a measured weight is 30 pounds too low. The same percent error would occur if the scale measured the mass to be 180 pounds.. Problems are available in worksheet 2.5.
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eople have a lot of trouble agreeing on a common format for things. Whether it is measuring distance, or the power adapter for your cell phone, there never seems to be uniformity. The SI (systeme internationale) units are about as close as scientists can come to agreeing on common units of measure. Listed are common units and prefixes Note the weird abbreviations- those are the most obscure aspects of this system.. measurement
SI Units unit
symbol
size
Unit Prefixes Prefix
mass volume distance amount brightness current time
kilogram liter meter mole candela ampere Second
kg L m mol cd A s
nano (n) micro (m) milli (m) centi Š kilo k) mega (M) giga (G)
billionth millionth thousandth hundredth thousand million billion
Scientific notation 10-9 10-6 10-3 10-2 103 106 109
Take a moment to familiarize yourself with these, then use this information to answer the questions below. 1. Speed is often expressed in miles per hour. However, using SI units, speed (velocity) is expressed in ____________ per ________, which is abbreviated as ________.
2. Volume is often expressed in ounces, however in SI units volume is expressed in _____________. 3. Complete the table Unit of measurement Length Mass Temperature density
We usually use
But SI units require
4. I have a 40 gigabyte hard drive. How many bytes is that? 5. Terabyte hard drives are available‌how many bytes of data do they hold?
6. Complete the table. Prefix Symbol
Factor
Scientific notation
example
Giga mega 1,000 centi 10-3 micro
Microgram n
4 (L1, honors only). Translate. For example 1000 kbytes = 1 Mbyte a. 1 kg = ___ g
b. 100 mm - ___ m
c. 100,000 cm = 1 ___
(1000 kilobytes= 1 megabyte)
d. 1,000,000 ncd = ______ cd
e. 1 mA = ____ nA
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If you are the type who enjoys mathematical formulas, this worksheet is for you. In each problem, you are given enough information to mathematically find a solution based on density and temperature. It helps to have a feel for the numbers as well: For both Density and temperature there are some benchmarks provided to warn you if your numbers are way off.
Common densities in grams per mL 0.001 air
0.7 gasoline
1.0 water
2.7 Aluminum
7.8 iron
11.3 lead
21.4 platinum
Example. What is the density of a sample that has a volume of 12 mL and a mass of 19 grams? Solution:
đ?‘‘đ?‘’đ?‘›đ?‘ đ?‘–đ?‘Ąđ?‘Ś =
đ?‘šđ?‘Žđ?‘ đ?‘ đ?‘Łđ?‘œđ?‘™đ?‘˘đ?‘šđ?‘’
=
19 đ?‘”đ?‘&#x;đ?‘Žđ?‘šđ?‘ 12 đ?‘šđ??ż
=
đ?&#x;?. đ?&#x;” đ?’ˆđ?’“đ?’‚đ?’Žđ?’” đ?’Žđ?‘ł
1. What is the volume of a sample that has a mass of 21 g and a density of 4 g/mL?
4. What is the mass of a sample of aluminum with a volume of 150 mL?
2. A liquid with a mass of 14 g is placed in a 50 mL graduated cylinder. The water rises from 20 to 41 mL. What is the density of the liquid?
5. The temperature in degrees Celsius is 273.15 degrees lower than Kelvin: K = 273.15 + C. Convert the following common Celsius temperatures to Kelvin: Room temperature: 24 oC Freezing point of water: 0 oC Boiling point of water: 100 oC Absolute zero: -273.15 oC:
3. A solid material that is insoluble in water has a volume of 35 mL and a mass of 39 grams at room temperature. Will it float in water?
6. Ethanol has a melting point of 150 K and a boiling point of 351 K. Convert these to degrees Celsius.
Example: Convert 298.15 Kelvin to OF Solution: đ??ž đ?‘Ąđ?‘œ đ?‘‚đ??ś đ?‘Ąđ?‘œ đ?‘‚đ??š; đ??ž = đ?‘‚đ??ś + 273.15; đ?‘‚đ??š
7. Convert 100 OF to OCelsius
8. Convert 100 OC to OF
=
đ?‘‚đ??ś
đ?‘Ľ
9 + 32 5
đ?‘‚đ??ś
= đ??ž − 273.15 = 25.000 OC
= 77 OF
9. Convert 474 K to OC.
L1, Honors only: 10. Give the boiling point of Aluminum (2467.0 OC) in OF and K.
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Scientific notation is handy for very large and very small numbers. Use the examples to help solve the problems given. Example 1: There were 34, 421 fans at Fenway park. Convert to scientific notation Solution: convert to a number between 1 and ten and then count up the powers of ten.
34,421 fans= 3.4421 x 104 fans Example 2: The sample had a mass of 0.000321 grams. Convert to scientific notation Solution: convert to a number between 1 and 10 and count up the powers of ten. 0.000321 grams= 3.21 x 10-4 grams Example 3: The student wrote “I will never be late to class again� 2.13 x 104 times on the chalkboard. Convert to a regular number (standard notation). Solution: Move the decimal place x number of places for 10x. In this case we move it four places to the right (if it is negative go to the left). 2.13 x 104 times= 21,300 times Note how in all cases the units (fans, grams, times) are included. Please convert the following to scientific notation. 1. 0.000058 inches ____________________ 2. 5,798 grains of sand ____________________ 3. 854,231 Obama voters ____________________ 4. 0.936421 seconds ____________________ 5. 1,200,000 miles ____________________ 6. 0.285438563 kilograms ____________________ 7. 4.000000092 grams ____________________ 8. 26 students ____________________
Please convert the following to standard notation. 9. 5.8 x 10-5 inches ____________________ 10. 5.798 x 104 grains of sand ____________________ 11. 8.546283 x 107 Obama voters ____________________ 12. 2.178 x 10-9 seconds ____________________ 13. -3.2 x 108 OC ____________________ 14. 5.2 x 108 cows ____________________ 15. Fix and convert: 35.4 x 104 electrons ____________________
L1, honors only: Please fill in the blanks using scientific notation. 9.The Sun has a diameter of about 1,392,000 kilometers (___________ meters), and its mass is about 200,000,000,000,000,000,000,000,000,000 kilograms ( ________________ grams). The surface temperature is 5778 K (________________ OF). Show your temperature calculation clearly below:
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This worksheet is designed to show how to convert units, and provides some assistance. See the introduction for a good example of a unit conversion that was never performed, with serious (125 million dollars!) consequences. We will be converting units throughout the year, so it is essential that you learn how to set up your equations and properly cancel units. Example 1: How many weeks are in 21 days? Solution: 21 đ?‘‘đ?‘Žđ?‘Śđ?‘ đ?‘Ľ
1 đ?‘¤đ?‘’đ?‘’đ?‘˜ 7 đ?‘‘đ?‘Žđ?‘Śđ?‘
= 3 weeks
Example2: How many Euros are in 20 dollars (1 Euro currently = 1.34 dollars)? Solution: 20 đ?‘‘đ?‘œđ?‘™đ?‘™đ?‘Žđ?‘&#x;đ?‘ đ?‘Ľ
1 đ??¸đ?‘˘đ?‘&#x;đ?‘œ 1.34 đ?‘‘đ?‘œđ?‘™đ?‘™đ?‘Žđ?‘&#x;đ?‘
Note that all unit conversions: 1. Begin with what you are given (in this case 21 days) 2. Multiply by conversion factors to convert units (in this case 1 week = 7 days). 3. Units are cancelled to make sure everything is set up properly (days/days = 1).
= 3 weeks
Convert three miles per hour to meters per second, where 1609 meters = 1 mile, and 3600 seconds = 1 hour Solution:
3 đ?‘šđ?‘–đ?‘™đ?‘’đ?‘ â„Žđ?‘œđ?‘˘đ?‘&#x;
đ?‘Ľ
1609 đ?‘šđ?‘’đ?‘Ąđ?‘’đ?‘&#x;đ?‘ 1 â„Žđ?‘œđ?‘˘đ?‘&#x; đ?‘Ľ 3600 đ?‘ đ?‘’đ?‘?đ?‘œđ?‘›đ?‘‘đ?‘ đ?‘šđ?‘–đ?‘™đ?‘’
=
đ?&#x;?.đ?&#x;‘đ?&#x;’ đ?’Žđ?’†đ?’•đ?’†đ?’“đ?’” đ?’”đ?’†đ?’„đ?’?đ?’?đ?’…
Please solve each problem using the same work shown in the examples, including cancelled units. No credit is given if the work is not shown. 1. How many weeks are there in 31 days?
3. Convert 65 miles per hour to meters per second, where 1609 meters = 1 mile, and 3600 seconds = 1 hour
2. How many days are there in 42 weeks?
3. Convert 333 meters per second to miles per hour, where 1609 meters = 1 mile, and 3600 seconds = 1 hour
3. There are 2.54 centimeters in an inch. How many centimeters are in six inches?
6 (l1, honors only). Convert 35 nm/ms to miles per hour; give your answer in scientific notation.
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For this final worksheet (L1, honors only) we consider how to work with the data in a scientific experiment: data that if properly handled could lead to an important discovery. How precise is your data? How many digits should you be using? Is there a pattern to your data that can be summarized in a formula? And, perhaps most importantly, how far off is your data from known values? These are some of the questions that comprise the topics of significant figures, formula derivation, and percent error calculations.
Significant figures Here are some general rules to help determine the level of precision that is appropriate for your data: 1. When taking a measurement, a good scientist will estimate one digit beyond the graduations for an analog instrument. For example if a 100 mL graduated cylinder has lines for each mL, volume may be reported to the tenth of a mL. Note that this doesn’t apply to digital instruments. 2. When adding or subtracting data, it makes sense to maintain the lowest level of precision (decimal places). For example if two measurements are taken in an experiment using two different balances, where one balance is accurate to the milligram (0.001 g) but another is only accurate to only the tenth of a gram, the final data should only be reported to the tenth of a gram. 3. When multiplying or dividing numbers, maintain the lowest number of significant figures. Significant figures are the numbers that matter. Consider this number: 0.032106000 seconds All of the nonzero numbers are significant- you can’t report that data without them. The two leading zeros aren’t significant- they would be dropped when converting to scientific notation. The central zero is significant; it can’t be eliminated. The final three zeros are significant; the scientist measured this data to the billionth of a second, and obtained 0 for the last three digits. The scientist wants you to know that. Similarly, 300. has three significant figures, but 300 (no decimal place) has only one; they may have been counting by hundreds. 0.032106000 has 8 significant figures. 4. If data needs to be rounded off and the digit in question is a 5, in this class we round up. For example, to report 4.35 inches using two significant figures, we use 4.4 inches.
Deriving Formulas Scientists clued in a long time ago to the fact that the world as we know it often displays mathematical precision. For example, a balloon gets large as it is heated; Double the temperature and the volume doubles. Observing that may be straightforward, but expressing it mathematically can be more challenging (see Charles Law to learn more). Other less obvious examples, such as E= mc2, tell us precisely how our world behaves with remarkable brevity.
Percent Error Scientists are always struggling to optimize the precision and accuracy of their data. When their data is off, they do a percent error calculation to see how bad their data is. A model that students can relate to is a test score. On a 100 question test, if your answered 87 questions correctly, your percent error is 13%. How did you do if your score is 87 correct on a 93 question test? Much better! The formula that sums it up is đ?‘’đ?‘&#x;đ?‘&#x;đ?‘œđ?‘&#x; đ?‘ƒđ?‘’đ?‘&#x;đ?‘?đ?‘’đ?‘›đ?‘Ą đ??¸đ?‘&#x;đ?‘&#x;đ?‘œđ?‘&#x; = x 100 đ?‘Žđ?‘?đ?‘?đ?‘’đ?‘?đ?‘Ąđ?‘’đ?‘‘ đ?‘Łđ?‘Žđ?‘™đ?‘˘đ?‘’ 13
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For the 100 point test this works out to 100 x 100 = 13%; error; for the 93 point test the percent error is 93 x 100 = 6.5%
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Significant figures
1. Assuming cm, provide measurements for A, B, C, and D A_________ B__________ C__________ D __________ 2. How many significant figures does each number have? (note that some numbers can have an infinite number of significant figures). 3.16 inches _________ 4 people _______ 0.034 g/mL ________ -32 OF _____ 3. Calculate and give your answers using the correct number of significant figures or level of precision: a. 3.2 + 4.44 = __________ b. 3.2 + 4.45 = __________ c. 3.6 x 4.18 = __________ d. 0.0329/65,329 e. 300 x 2.4 = _____
Deriving formulas. 4. You observe that for a mentos eruption, each time you double the number of mentos, the height of the eruption doubles. Express this using a mathematical formula.
5. You observe that when the diameter of your soda bottle nozzle doubles, the height of your mentos eruption is cut in half. Express this using a mathematical formula.
Percent Error 4. You earn a score of 4 on a 5 point test. What is your percent error?
5. You know that your height is 5 feet7 inches, but a nurse records it as 5 feet 9 inches. What is the percent error?
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In this our second unit, we began with the Mentos Eruption lab, where each of you had the goal of discovering something new about this phenomenon. To accomplish this each group designed and carried out experiments that generated data, and that data was the evidence for your discovery. For some of you, if your data was reliable and precise, you were able to summarize your discovery with a mathematical formula- a major accomplishment. You published your work, carefully describing the state of the art prior to your discovery relying only on verifiable, peer reviewed sources of information.
Whenever a scientist is attempting to understand or discover something, the data is the foundation. In this unit we explored all aspects of data: The units that are recommended (SI units) to keep everyone on the same page The prefixes that can be tacked on to the front of the units to define the scale of those units Those units that are combined from individual ones such as density, and how to apply those formulas How to interconvert common units of temperature How to report very large and small numbers using scientific notation How to consider the precision and accuracy of your data and apply the rules of significant figures when reporting results Finally, how to look for patterns in your data that may be summarized using mathematical formulas. To ace the data test you should Read the data packet and all the required reading assignments.. Review the mentos eruption lab, and consider how your data contributes to a scientific discovery Review the data lecture, watch the screencasts if necessary, and complete the associated worksheets Complete the review questions which follow. 1. Data Analysis SI units: a. time_____ b. length _____ c. mass _____ d. temperature, _____ e. amount, _____ f. density, _____ g. volume _____ h. luminous intensity _____
2. Prefixes: a. giga _____ b. mega _____ c. kilo _____
d. Deci (omit) e. milli _____ f. micro _____ g. nano _____ h. pico _____ i. List the units from pico to giga _______________________________________________________________
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3. Density equation and problems: d = m/v Example: What is the density of a substance with a mass of 2.4 grams and a volume of 3.2 mL?v True or false: The question above is a unit conversion problem. True or false: d = mv? True or false: v = md?
4. Kelvin to Celsius temperature equation and problems K = oC + 273 Example: 298 K = _____oC. 5. Scientific Notation (L1 only) Example : Convert 6.2 x 10-4 to a regular number :__________ 6. Percent Error a. What is the formula for percent error? Example: If I have a mass of 142 pounds, but my balance says my mass is 152 pounds (ouch!), what is the percent error of that balance? 8. Significant Figures (L1 only) Example : 3.21 has ___ significant figures 7. Unit conversion Example : 3.201 has ___ significant figures Show your work below : a. 12 kg = _____g Example : 0.321 has ___ significant figures Example : 3.210 has ___ significant figures b. 3 hours = ________ seconds Example : 3.21 x 2.4 has ___ significant figures Example : 3.21 + 4.234136 has ___ significant figures Give the answers using the correct number of significant c. 36 dozen eggs = __________ eggs figures (L1 only) a. 3 + 2 = ________ b. 3.0 + 5.000 =________ d. 25 miles = ____________ meters c. 14.21 x 32.4809 =________ d. 15.5112123 + 4 =________ e. What is the volume of a piece of metal that has a mass of 3.2 e. 36 miles/hour = ________meters/second grams and a density of 2.703 grams per cubic centimeter ? ________ F (L1, honors only). 3.2 x 10-23 picometers/year = _________miles/hour
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