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23 Feb 2006  23:05
dimensional analysis word problems & answers
They're hard to come by. Here's a pretty good selection for kids in the 4th to maybe 8th grade range. (Actually, you could use these problems with any beginner.) I've included everything inside this post, but I've also created separate pages that ought to be easy to print out, using the 'printable' tab at the top of the screen. (I think these two pages are editable by everyone, so you ought to be able to add your own problems, take problems away, increase or decrease the space between items, etc.
For future reference, all of these pages can be found in math lessons and in the BookStyle Index.
1 kilometer = 0.6 miles 2. The deepest part of the ocean is the Marianas Trench; its depth is 11.03 km. How many feet is that? 3. The largest whale measured 33.27 meters in length. How many feet is this? 4. The average temperature of the oceans is 3.9° C. What is this in Fahrenheit? 5. The highest tides on planet Earth occur near Wolfville, in Nova Scotia’s Minas Basin. The water level at high tide can be as much as 16 meters higher than at low tide! How many feet is this? 6. Sunlight only reaches 30 to 120 meters under the waves. Convert this to feet. 7. A blue whale can weight up to 280, 000 pounds. That’s larger than the largest dinosaur. How many kilograms is that? (Round your answer to the nearest whole kg.) 8. Previous studies suggest that the expected global warming from the greenhouse effect could raise sea level approximately 100 centimeters in the next century or two. What is this in feet? 9. If all the ice in glaciers and ice sheets melted, the sea level would rise by about 80 meters, or how many feet? 10. The longest river is the Nile River, in Egypt, Africa. It is 4,160 miles long and flows northward into the Mediterranean Sea. How long is it in km?
copyright © 2001 Gisele Glosser
(from Math Goodies  can’t find URL, but Gisel Glosser seems to have worksheets posted at schoolhousetech)
1. Convert 640 ounces into pints.
2. If 20 shillings equal 1 pound, how many shillings does 1000 pounds equal?
1. How many seconds are there in 1.2 weeks?
2. If a recipe calls for 37 grams of sugar, how many pounds does that correspond to?
Carolyn & Bernie are going to buy a new car, which they will drive 13,000 miles a year. An example of the kind of math my job requires:
2.2 pounds = 1 kilogram You need to administer an IV drug to a dog. Part 1: The dosage is 20mg per kg of body weight. The drug is in a solution of 5g per 1 Liter. The dog weighs 66lbs. How many mL of solution do you need? Part 2: IV drugs can be administered using a drip set which delivers a set quanity of liquid at an adjustable rate.
You need to administer the drug over a period of 4 hours. Your drip set delivers 1mL of liquid per 8 drips. At what rate (in drips per minute) do you need to set your drip set?
The Adams' car has a 16gallon gas tank. How many tanks of gas will the car use on a 2000mile trip if the car averages 25 miles per gallon? answers to Gisele Glosser's problems:
1.Convert 640 ounces into pints.
2. If 20 shillings equal 1 pound, how many shillings does 1000 pounds equal?
1. How many seconds are there in 1.2 weeks?
1 week = 7 days
2. If a recipe calls for 37 grams of sugar, how many pounds does that correspond to?
37 g x 1 lb/453.59 g = 8.2 x 102 lb
Chem 192 problems:
The Adams' car has a 16gallon gas tank. How many tanks of gas will the car use on a 2000mile trip if the car averages 25 miles per gallon?
Back to main page. CommentsAfter entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.Please consider registering as a regular user. Look here for syntax help. HEY! You are awesome! These are perfect for the unitconversionworkoutweekend Ben will be having this weekend.  CarolynJohnston  24 Feb 2006
Good practice, although I have a minor correction and a few quibbles:  Unit in answer to Gisele's number 7 given as feet instead of kilograms.  Donna's first problem is not completely specified: Ounces generally refers to weight, but can be troy or "regular" (avoirdupois)  volume is measured in fluid ounces, plus US and UK fluid ounces are slightly different. Likewise, while pint is always a volume measurement, there are UK pints, US fluid pints, and US dry pints, all slightly different. This question illustrates one of the reasons why the metric system is often portrayed as superior to "traditional" measurement systems  there is no confusion about which units are which.  Also, in recipies (at least in the US) sugar is usually measured by volume, unless the recipie calls for a LOT of sugar (a pound or more) so this is an unlikley conversion.  AndyLange  24 Feb 2006
A practical problem, to show why you might want dimensional analysis even if you're a "gearhead". You are almost finished working on your BMW, and the shop manual says to tighten the last bolt to 7 Nm (Newtonmeters). Your torque wrench is calibrated in footpounds. What should you set your torque wrench to? 1 N = 0.225 lbs. 1 m = 3.28 ft.
Answer: 7.00 Nm * 0.225 lbs/N * 3.28 ft/m = 5.17 ft.lbs. (Note that all terms are rounded to three significant digits.) Tricky aside: 1 N = 1 kg*m/sec^{2} But you can't do a direct conversion from kg (weight) to lbs. As used here, kg is a measure of mass, and lbs. is a measure of force. You would need to add in gravitational acceleration to convert from one to the other. One pound is the force exerted by one slug (approximately 32.2 pounds mass) when accelerated at 1 foot/sec^{2}.  DougSundseth  24 Feb 2006
That gravitational constant will get you every time. Just like the confusion between pounds force and pounds mass, there is confusion over whether to interpret kg (in the real world) as a mass or force. In many technical articles I read, authors are very sloppy about this. Another big problem is density, often described by the greek letter rho, which should be based on mass. If you want a weight density, you are really talking about rho * g. You have to look carefully at the units and assume nothing. Keep in mind that dimensional analysis is not just doing unit conversions. It is using units to make sure that you have your equations correct. The formal process of dimensional analysis is about using this idea to create correct equations. As I mentioned before, it is quite magical to see how this works.
 SteveH  24 Feb 2006
I always thought unit conversion problems were a lot of fun. An example of the kind of math my job requires:
2.2 pounds = 1 kilogram You need to administer an IV drug to a dog. Part 1: The dosage is 20mg per kg of body weight. The drug is in a solution of 5g per 1 Liter. The dog weighs 66lbs. How many mL of solution do you need? Part 2: IV drugs can be administered using a drip set which delivers a set quanity of liquid at an adjustable rate. You need to administer the drug over a period of 4 hours. Your drip set delivers 1mL of liquid per 8 drips. At what rate (in drips per minute) do you need to set your drip set?
 LesleyStevens  24 Feb 2006
These are perfect for the unitconversionworkoutweekend Ben will be having this weekend. YAY! I'm glad you liked them. It took me HOURS to do this post..... ayyiyi as Ricky Ricardo would say...  CatherineJohnson  24 Feb 2006
I'm going to add your car problem to the list.  CatherineJohnson  24 Feb 2006
Extra credit for adults. Given that 1 inch = 2.54 centimeters (by definition) http://scienceworld.wolfram.com/physics/Inch.html what are the exact relationships between miles and kilometers? The values above are quite close but not exact.
 SusanJ  24 Feb 2006
Can someone check my answer to Carolyn's problem?  CatherineJohnson  24 Feb 2006
yeah, I took Gisele's answer off my own answer sheet  didn't check to see if the number was right, though   CatherineJohnson  24 Feb 2006
Carolyn's problem does not have enough information. The question asks, "if gas goes up to $4 per gallon, how much money will they save," but does not state what the current price is. Do you mean, "Assuming that gas costs $4 per gallon, how much cheaper is the gas cost per year to operate the Civic?" There are other cost factors involved, as well. Caravans probably cost more in repairs  I read horror stories online about how they basically stop running after 150K miles, whereas a Honda is just getting warmed up at 150K. The comprehensive insurance is probably higher for the Civic, since they are more frequently stolen than are Caravans.
 GoogleMaster  24 Feb 2006
Lesley I love that problem!
 CatherineJohnson  24 Feb 2006
Carolyn's problem does not have enough information. Hey, how did this become MY problem? It's not my problem. I have no problems.  CarolynJohnston  24 Feb 2006
I have no problems. That's only if you traded the Caravan for the Civic. ;)  GoogleMaster  24 Feb 2006
An nonmetric unit of length, originally defined as the lengths of three "average size" barleycorns laid endtoend, but now more rationally defined as 2.54 cm. An older definition no longer used was 1 meter = 39.37 inches, giving 2.54000508 cm/inch. 12 inches are called 1 foot.  CatherineJohnson  24 Feb 2006
Does this mean that we need to trade in our old yardsticks? Or our metersticks?  GoogleMaster  24 Feb 2006
Probably both, unless your meterstick is fairly new. From the NIST web page, as of 1980 the definition of a meter was changed to: The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. Actually, I wouldn't bother with a tradein unless your yardstick or meterstick can be read to 2 parts in a million. None of mine are that precise.  AndyLange  26 Feb 2006
"The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second." Beats trekking to the North pole. 1/10,000,000 of the distance between the equator and either pole  CharlesH  26 Feb 2006
That's only if you traded the Caravan for the Civic. ;) We did (get a civic instead of a caravan).  CarolynJohnston  26 Feb 2006
 
