Harvard Bridge, which connects MIT with its fraternities across the Charles Rive

Question

Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The units of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police could not easily interfere. (Presumably, the police were originally upset because a Smoot is not an SI base units, but these days they seem to have accepted the units.) The figure shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of 45.0 Smoots in (a) Willies and (b) Zeldas?

Explanation / Answer

Unit conversions are easy. To convert from a unit A to a unit B you multiply a ratio of B units to A units that makes the actual quantity they represent equal. So, for example, if, 5 unit B = 2 unit A x unit A * (5 unit B / 2 unit A) = y unit B Notice that, the unit A in the numerator cancels with the unit A in the denominator. That's how you know you're doing it right, and you're fraction is not flipped (the reciprocal). So, for example, in the example I gave: x * (5 unit B / 2 ) = x * (5 unit B / 2) = x * (5/2) unit B

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