Dimensional Analysis of a lens

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SUMMARY

The discussion focuses on dimensional analysis, specifically converting the area of a telescope lens from square millimeters to square feet. The area given is 7903 mm², and the conversion process involves using unit equivalency relationships, such as 1000 mm = 1 m, 1 m = 100 cm, 2.54 inches = 1 cm, and 12 inches = 1 ft. Additionally, the discussion addresses the time required for a technician to polish the lens, which is calculated based on the rate of 45 seconds for 135 mm².

PREREQUISITES
  • Understanding of dimensional analysis and unit conversions
  • Familiarity with area measurement units (mm², ft²)
  • Basic knowledge of metric and imperial unit relationships
  • Ability to perform multiplication and division with units
NEXT STEPS
  • Study dimensional analysis techniques in chemistry
  • Learn about unit conversion methods for area measurements
  • Explore practical applications of dimensional analysis in scientific calculations
  • Practice problems involving unit conversions in physics and engineering contexts
USEFUL FOR

This discussion is beneficial for undergraduate chemistry students, educators teaching dimensional analysis, and anyone needing to perform unit conversions in scientific contexts.

metalmagik
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Hello everybody, I am taking a basic undergrad General Chemistry I course and am just having a little trouble brushing myself up on dimensional analysis (or factor label). This is the problem.

The area of a telescope lens is 7903 mm2. (a) What is the area in square feet? (b) If it takes a technician 45 sec to polish 135 mm2, how long does it take her to polish the entire lens?

I am just not so sure how to get from millimeters squared to square feet. If anyone can help me out I'd really appreciate it. Thank you.
 
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Part (a) --- Note carefully, you have millimeters*millimeters, and you want to convert to feet*feet.
1000 millimeters = 1 meter
1 meter = 100 centimeters
2.54 inches = 1 centimeter
12 inches = 1 foot.
 
Oh I see, so do I simply treat it as 1000 millimeters * 1000 millimeters and so on with the conversions?
 
Each units equivalence relation is used as a ratio in your conversion calculation. You do not start with 1000 mm * 1000 mm [excuse the abbreviations], but you are starting with 7903 mm*mm [or in lengthy expressiveness, 7903 * millimeters*millimeters]. Use the unit equivalency relationships from there.
 

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