Dimensional Analysis of a lens

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Discussion Overview

The discussion revolves around a dimensional analysis problem related to converting the area of a telescope lens from square millimeters to square feet and calculating the time required to polish the lens based on a given rate. The scope includes mathematical reasoning and conceptual clarification of unit conversions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving the conversion of area from square millimeters to square feet and the time required for polishing.
  • Another participant provides a series of unit equivalences necessary for the conversion process, emphasizing the need to convert millimeters squared to feet squared.
  • A subsequent participant seeks clarification on whether to treat the area as 1000 mm multiplied by 1000 mm for the conversion.
  • A later reply corrects this approach, stating that the conversion should start with the area value of 7903 mm² and apply the unit equivalency relationships appropriately.

Areas of Agreement / Disagreement

Participants appear to agree on the need for unit conversions but have not reached a consensus on the specific method for performing the conversion calculations.

Contextual Notes

There are limitations regarding the clarity of the conversion process, as participants express uncertainty about the correct approach to dimensional analysis and the application of unit equivalencies.

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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