Dimensional Analysis s1

Dimensional Analysis

Why? All measurements contain a numerical value and a unit. It is possible to change or convert units on a measurement without changing what the measurement represents. For example, if you spend 1 hour doing chemistry homework tonight, you could say you spent 60 minutes doing homework. The amount of time you worked is constant; the only difference is the unit you choose to report the time you spent on homework. Dimensional analysis is a tool that can be used to convert units of measure. This tool can be used to solve various chemistry related (and non-chemistry related) problems.

Model 1

1) In the drawing above, how may pounds of apples does the shopper want to buy?

2) Identify the conversion factor in the model (HINT: Look in the buyer’s thought bubble).

3) Below are examples of other conversion factors.

1 hour 60 seconds 1 day 365 days 60 minutes 1 minute 24 hours 1 year

Using one grammatically correct sentence, describe a unique characteristic of a conversion factor. (In other words, how can you recognize a conversion factor when you see one?) 4) If the unit “pounds” is used in the problem, why does “pounds” disappear in the final answer of $3.98? Give a mathematical reaction, using grammatically correct sentences in your explanation.

5) What is the unit in the final answer? Why does this occur?

6) Suppose another market offered five pounds of apples for $6. Show using a mathematical equation (much like the one in Model 1) how the buyer would do this problem. Provide the answer with the correct units.

7) How much will the buyer save by switching to the other market?

Model 2

8) Based on Model 2 above, complete the following equality statements:

1 in = ______cm

______in = 1 foot 9) Write each of the equalities above in the form of a fraction.

10) Houston Rockets basketball player Yao Ming is about 7.5 feet tall. Show using a mathematical equation (as in Model 1) how you can use the information above (in question 8) to calculate his height in inches. This setup should ALWAYS INCLUDE UNITS.

11) Using the same kind of setup, convert your answer in question 10 to centimeters. This set up should ALWAYS INCLUDE UNITS!

12) Each of the calculation in questions 10 and 11 were single-step conversions. We can combine the two problems to make one multi-step problem. By filling in the blanks, use the following multiple-step ste up to convert Yao Ming’s height from feet to centimeters. Remember, this setup should ALWAYS INCLUDE UNITS! (Hint: What unit will be at the beginning? What unit will be at the end?)

______x ______x ______= ______

13) Based on question 12, what kind of information did you use first to start the setup of your problem (measurement or conversion factor)? What comes after that information in the setup?

14) Do you think setting up the problem in a certain order helps you solve the problem? Explain.

Extension Questions

1) You spend 50 minutes in chemistry class on a regular schedule day.

2) Calculate the cost of gasoline for a 420 mile trip if your car averages 20 miles/gallon of gas, and the gas costs $2.85/gallon.

3) Harold’s car has a fuel efficiency of 35 miles per gallon. Kumar’s car has a fuel efficiency of 12 kilometers per liter. Who gets better gas mileage, Harold or Kumar? (Hint: 1 mile = 1.609 km and 1 gallon = 3.79 liters.)

4) A unit of length called the “furlong” is used in horse racing. The units of length called the “chain” and “link” are used in surveying. There are 8 furlongs in 1 mile, 10 chains in 1 furlong, and 100 links in 1 chain. What is the length of 1 link in inches? Report your answer to 3 significant figures.