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Phy 121
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** Question Form_labelMessages **
SI Units
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Book Problems 12-15 regarding SI Units from A0 and A1
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I just have a question regarding SI Units. Are there a list of conversions we should know? I actually struggled a little on the first book problems. I was not aware of the conversion factors for the given numbers. I am aware of the SI Base Quantities and Units, by looking at the table on pg 10. I just wanted to know if you could tell me the conversion factors you expect us to know for tests or upcoming assignments.
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You won't need to know a lot of SI conversions for the test. Of course you will know how to convert between meters and centimeters and such--the basic metric units.
You won't need it on the test, but as general knowledge you should also know that
1 inch = 2.54 centimeters.
Using just this you should be able to convert inches, feet and miles to centimeters, meters, kilometers, etc..
For example you would know how many meters in a kilometer, how many centimeters in a meter, how many inches in a centimeter, how many inches in a foot and how many feet in a mile. So you could figure out how many kilometers in a mile, or how many miles in a kilometer.
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Phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Percent Uncertainty
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Questions 2-5 on text-related problems:
2. What is the uncertainty in the following reported measurements, and what is the percent uncertainty in each?
• 5.8 centimeters
• 2350 kilometers
• 350. seconds
• 3.14
• 3.1416
3. What is the uncertainty in the area of a rectangle, based on reported length 23.7 cm and width 18.34 cm?
4. (Principles of Physics students are invited to solve this problem, but are not required to do so): What is the approximate uncertainty in the area of a circle, based on a reported radius of 2.8 * 10^4 cm?
5. What is your height in meters, and your ideal mass in kilograms? How much uncertainty do you think there is in each, and why?
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I am unsure of how to know what the uncertainty is. For the first problem it gave me the uncertainty of + - 0.1, how do I get an uncertainty if it is not given to me explicitly?
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A measurement of 5.8 centimeters could represent any length between 5.75 cm and 5.84999... cm. Any of these numbers would round off to 5.8 cm.
So we could say that a 5.8 cm measurement really means
5.8 cm +- 0.05 cm.
5.8 cm + 0.05 cm = 5.85 cm,
5.8 cm - 0.05 cm = 5.75 cm
and our length will be between these two extremes.
Another more standard interpretation is that the uncertainty is plus or minus one mark on the measuring instrument. So if the 5.8 cm was measured on a ruler marked in millimeters, the uncertainty would be +- 0.1 cm and our measurement would be represented at
5.8 cm +- 0.1 cm.
However we don't know what the instrument was. So we're left with some abmiguity.
In practice it would be up to you to make a reasonable judgement based on the actual situation.
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Another example: It's about 210 meters to the end of the road. That makes is about 210 000 millimeters to the top of the road.
However it would be ridiculous to think that the distance is known to within +- 0.5 millimeter. Just multiplying the 210 meters by 1000 doesn't change the uncertainty in the original result.
All those extra zeros are needed to express the distance in millimeters, but they are not significant in the sense of adding accuracy to our measurement.
If we had measured that distance to the nearest millimeter, we probably wouldn't have come out with four zeros at the end, but it's possible that we would have. In that case we would write our measurement as
210 000. millimeters. The . at the end of the number indicates that all digits up to that mark are significant.
Let's go back to the 210 meters. Had the result been written as 210. meters, then we would accept the measurement as being accurate to the nearest meter. However since it was written 210 meters, we do not assume that the 0 on the end is significant.
The uncertainty in the number 210 is therefore either +-5 or +-10, depending on what you might know about the measuring process.
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See what you can make of the remaining questions.
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