Sure! Here are some dimensional analysis problems that involve using the "Giant 1" technique. The "Giant 1" method helps ensure that units cancel appropriately, leading to a correct solution.

Problem 1: Converting Meters to Feet

Problem: Convert 5 meters to feet. (Use $1 \text{ meter} = 3.28084 \text{ feet}$)

Solution: $5 \text{ meters} \times \frac{3.28084 \text{ feet}}{1 \text{ meter}} = 16.4042 \text{ feet}$

Answer: 16.4042 feet

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Problem 2: Converting Kilograms to Pounds

Problem: Convert 10 kilograms to pounds. (Use $1 \text{ kg} = 2.20462 \text{ lbs}$)

Solution: $10 \text{ kg} \times \frac{2.20462 \text{ lbs}}{1 \text{ kg}} = 22.0462 \text{ lbs}$

Answer: 22.0462 lbs

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Problem 3: Converting Hours to Seconds

Problem: Convert 3 hours to seconds. (Use $1 \text{ hour} = 3600 \text{ seconds}$)

Solution: $3 \text{ hours} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} = 10800 \text{ seconds}$

Answer: 10800 seconds

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Problem 4: Converting Liters to Gallons

Problem: Convert 4 liters to gallons. (Use $1 \text{ liter} = 0.264172 \text{ gallons}$)

Solution: $4 \text{ liters} \times \frac{0.264172 \text{ gallons}}{1 \text{ liter}} = 1.056688 \text{ gallons}$

Answer: 1.056688 gallons

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Problem 5: Converting Celsius to Fahrenheit

Problem: Convert 25°C to Fahrenheit. (Use the formula $F = \frac{9}{5}C + 32$)

Solution: $F = \frac{9}{5} \times 25 + 32 = 45 + 32 = 77°F$

Answer: 77°F

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If you would like further details on any of these problems or have questions, feel free to ask!

Follow-up Questions:

1. What is the importance of dimensional analysis in physics and engineering?
2. Can you provide examples of complex conversions that require multiple unit conversions?
3. How do you apply dimensional analysis to verify equations?
4. What are some common mistakes to avoid when using dimensional analysis?
5. How does dimensional analysis help in understanding physical relationships in formulas?

Tip: Always ensure that the units you want to convert to are in the numerator, while the original units are in the denominator to facilitate cancellation.