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 64.0 Smoots in (a) Willies and (b) Zeldas?
The Correct Answer and Explanation is:
To convert 64.0 Smoots into Willies and Zeldas, we first need to establish the conversion rates among the three units: Smoots (S), Willies (W), and Zeldas (Z). While the problem does not provide these conversion factors directly, we can reasonably assume hypothetical conversion rates for the sake of this exercise. Let’s say:
- 1 Smoot = 2 Willies
- 1 Smoot = 4 Zeldas
Using these assumptions, we can calculate the length of 64.0 Smoots in both Willies and Zeldas.
(a) Conversion to Willies
Given that (1 \, \text{Smoot} = 2 \, \text{Willies}):
[
\text{Length in Willies} = 64.0 \, \text{Smoots} \times 2 \, \frac{\text{Willies}}{\text{Smoot}} = 128.0 \, \text{Willies}
]
(b) Conversion to Zeldas
Given that (1 \, \text{Smoot} = 4 \, \text{Zeldas}):
[
\text{Length in Zeldas} = 64.0 \, \text{Smoots} \times 4 \, \frac{\text{Zeldas}}{\text{Smoot}} = 256.0 \, \text{Zeldas}
]
Summary of Results
- The length of 64.0 Smoots is equivalent to 128.0 Willies.
- The length of 64.0 Smoots is equivalent to 256.0 Zeldas.
Explanation
The concept of using non-standard units of measure, such as Smoots, is a playful yet practical demonstration of how measurement can be made relatable and humorous within specific communities. The Smoot is a unique unit named after Oliver R. Smoot, providing a personal touch to the bridge’s measurements. This whimsical approach to measuring lengths shows how cultural and social activities, like fraternity hazing rituals, can intersect with mathematics and physics.
Conversions between non-standard units require a defined relationship to one another, just as we do with standard units like meters, feet, and inches. In this case, the fictitious conversions (2 Willies per Smoot and 4 Zeldas per Smoot) illustrate the necessity of having a clear understanding of the relationships between different units when making conversions. While the figures we used here were illustrative, in practice, accurate conversion factors would be necessary for precise calculations.