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Dimensional Analysis in Physics: Practical Applications and Problem-Solving Techniques

This lesson explores the integral role of mathematics in physics, focusing on dimensional analysis and its applications. Students will learn to analyze problems that involve units, measurements, and dimensions. The session includes a real-world example of measuring ingredients in a recipe, transitioning between standard and metric systems. We will discuss the importance of utilizing models, graphs, and the Greek letter symbols to represent mathematical operations effectively. By the end, students will be equipped to create and solve complex dimensional analysis problems.

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Dimensional Analysis in Physics: Practical Applications and Problem-Solving Techniques

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  1. “The Language of Physics” Physics 1.3

  2. I. Mathematics and Physics formula A. Using Models Model Data Table Graph

  3. 1. Which model is best? Why? 2. Graph – combination of visual and data 3. Greek letters – describe mathematical operations a. Σ (sum), ∆ (change)

  4. II. Dimensional Analysis • Def – a way to analyze and solve a problem that has units, measurements or dimensions. • Parts 1. Conversion Factor always equal to “1” numerator = denominator

  5. 2. Examples:  100 cm 1 meter 1 meter or 100 cm  1 foot or 12 inches 12 inches 1 foot

  6. 3 step Approach 1. Analyze – determine where you are and where you need to get to. 2. Calculate – use math skills 3. Evaluate – Does your answer make sense? -right # of sig figs -right units -reasonable -check your math

  7. III. Example Your school club has sold 600. tickets to a chili-soup fundraising event, and you have volunteered to make the chili. You have a chili recipe that serves 10. The recipe calls for 2 teaspoons of chili powder. How much chili powder do you need for 600 servings? 120. teaspoons of chili powder

  8. You decide that measuring 120. teaspoons would be too much work. Instead of using teaspoons you decide to use cups to measure out the chili powder. How many cups would you need to add? 3 teaspoons = 1 tablespoon 16 tablespoons = 1 cup 2.5 cups

  9. Physics 1.3 problem Create a complex dimensional analysis question scenario like we did with the chili cook off example in our notes that requires several steps. (You must have a switch between the Standard System and the SI/Metric System in your example)

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