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THE DREADED Dimensional Analysis

THE DREADED Dimensional Analysis. You decide to have a Pizza Party. How can you be sure things go smoothly?. http:// www.youtube.com/watch?v=geBJ5Qj4-G0. As with any party, there are a number of potential concerns; Drama No one coming Too many people coming = not enough food!.

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THE DREADED Dimensional Analysis

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  1. THE DREADEDDimensional Analysis

  2. You decide to have a Pizza Party. How can you be sure things go smoothly? http://www.youtube.com/watch?v=geBJ5Qj4-G0

  3. As with any party, there are a number of potential concerns; • Drama • No one coming • Too many people coming = not enough food!

  4. Some Data to Consider • How many pizzas are being ordered for Jimmy’s party? 8-10 (Assume 9) • If Miles (his frienemy) comes, there will be 24 total people present. • Assuming each person eats (on average) 2.8 slices of pizza, will Jimmy’s party have enough food to survive and remain drama-free? • Prove this for me mathematically either way at your seat.

  5. Is this possible? • Do we have enough information? • How many slices are there in 1 pizza? • Assume, for the sake of argument, there are 8 slices per pizza. • This ratio represents the key to solving this otherwise simple problem. 1 Pizza = 8 slices OR 8 slices = 1 pizza

  6. A Different Approach • How many pizzas do we have? 9 (Start with what you are given) • How many slices total? Use your ratios! • The ratio allows us to move from the units we’re given to the units we want. 9 pizzas x 8 slices = 72 slices (Units Cancel) 1 pizza

  7. So, what do we know? • 72 total slices of pizza at the party • How many will be theoretically eaten? • There are 24 people attending • The useful ratio in this case is 1 person = 2.8 slices OR 2.8 slices = 1 person 24 people (persons) x 2.8 slices = 67.2 slices 1 person

  8. THE METHOD • Start with what your given • Determine the appropriate ratio for the situation. • The units that we want to cancel go on the bottom while the units we want to keep go on top. • Multiply everything on top; divide by everything on the bottom

  9. Dimensional Analysis EX1 • These both give us a relationship between in. and ft. • We use D.A. to cancel units • How many inches in 2ft? COPY THE METHOD WE USE, it will get complicated later.

  10. Dimensional Analysis EX1 • The units cancel out leaving only • Giving us an answer of 24 in.

  11. Dimensional Analysis EX2 Show the correct work! • Convert 48 pounds to ounces.

  12. Dimensional Analysis EX3 Show the correct work! • Convert 5 days to hours.

  13. Dimensional Analysis EX4 Show the correct work! • How many seconds are there in 4 minutes?

  14. Dimensional Analysis EX5 Show the correct work! • If a car is traveling 24.2 miles/hour, what is its equivalent speed in feet/second?

  15. Dimensional Analysis EX6 Show the correct work! • A solid rock occupies a volume of 97.8 cubic centimeters. What is its equivalent volume in cubic meters?

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