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Chapter 1: Problem 4

The speed of light is \(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Convert this to furlongs per fortnight. A furlong is 220 yards, and a fortnight is 14 days. An inch is \(2.54 \mathrm{~cm}\).(answer check available at lightandmatter.com)

Short Answer

Expert verified
The speed of light is approximately \(1.803 \times 10^{12}\) furlongs per fortnight.

Step by step solution

01

Convert meters to inches

First, we need to convert meters into inches. Since 1 meter is equal to 100 cm, and 1 inch is equal to 2.54 cm, we can use the conversion factors: \[ 1 ext{ meter} = \frac{100 ext{ cm}}{2.54 ext{ cm/inch}} \approx 39.3701 ext{ inches} \]
02

Convert inches to yards

Next, convert inches to yards, knowing that there are 36 inches in 1 yard: \[ 39.3701 ext{ inches} = \frac{39.3701}{36} ext{ yards} \approx 1.09361 ext{ yards} \]
03

Convert meters to furlongs

Now, we use the fact that 1 furlong is 220 yards to convert from meters to furlongs: \[ 1.09361 ext{ yards} = \frac{1.09361}{220} ext{ furlongs} \approx 0.00497142 ext{ furlongs} \] Thus, 1 meter approximately equals 0.00497142 furlongs.
04

Convert speed of light to furlongs per second

Convert the speed of light into furlongs per second using the conversion in the previous step:\[ 3.0 \times 10^{8} ext{ m/s} \times 0.00497142 ext{ furlongs/meter} \approx 1.491426 \times 10^{6} ext{ furlongs/s} \]
05

Convert seconds to fortnights

Finally, convert seconds into fortnights. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 14 days in a fortnight. Therefore, a fortnight is:\[ 14 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 1,209,600 \text{ seconds} \] Now, use this conversion to find furlongs per fortnight:\[ 1.491426 \times 10^{6} ext{ furlongs/sec} \times 1,209,600 ext{ seconds/fortnight} \approx 1.803 \times 10^{12} ext{ furlongs/fortnight} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Speed of Light
The speed of light is one of the most fundamental constants in physics. It is the speed at which light travels through a vacuum, and is approximately \(3.0 \times 10^8 \text{ meters per second (m/s)}\). This incredible speed is how fast all electromagnetic waves, including radio waves and visible light, travel through space. Understanding the speed of light is crucial for various scientific disciplines, including physics and astronomy. It allows scientists to calculate distances in space, as well as the time it takes for light to travel between objects. Light speed is often used as a universal speed limit in the theory of relativity, beyond which objects cannot travel. However, the speed can be somewhat abstract because it is so immense. By converting it into different units of measure, like furlongs per fortnight, we can contextualize it in more relatable terms. This conversion helps us appreciate just how fast the speed of light really is by comparing it to more everyday units defined by distances and times familiar to us.
Metric to Imperial Conversion
When converting units, it's crucial to understand how the metric system compares to the imperial system. The metric system, used worldwide, is based on powers of ten. This makes conversions within the metric system quite straightforward. In contrast, the imperial system is used mainly in the United States and can be more complex. For this exercise, it's essential to convert meters into yards, then into furlongs, and seconds into fortnights. Here鈥檚 how you can carry out some of these conversions:
  • Meters to Inches: 1 meter is approximately 39.3701 inches because 1 meter equals 100 cm and 1 inch equals 2.54 cm.
  • Inches to Yards: Since there are 36 inches in a yard, divide the number of inches by 36 to get yards.
  • Yards to Furlongs: A furlong is 220 yards, so divide the yards by 220 to convert to furlongs.
Understanding these conversion steps can be handy for calculations in fields such as engineering, where both metric and imperial measurements are often used. Knowing how to switch between these units ensures precision and accuracy in calculations.
Furlongs and Fortnights
Furlongs and fortnights may seem like antiquated or whimsical units, but they have historical significance and are still used in some contexts today.
  • Furlongs: Originating from "furrow long," a furlong is a distance measurement used primarily in horse racing. It measures 220 yards or about 201.168 meters.
  • Fortnights: Derived from the Old English "feowertyne niht," meaning "fourteen nights," a fortnight is a time period of 14 days. It鈥檚 a unit that is less commonly used today but can be handy for contextual historical settings or expressions.
Converting modern scientific measurements, like the speed of light, into furlongs per fortnight requires grasping both these units to do the conversion accurately. This exercise exemplifies how diverse our measurement systems can be and highlights their historical roles. Understanding these units provides insights into both the history of measurements and practical applications, like expressing speeds or durations in creative ways.

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Most popular questions from this chapter

(solution in the pdf version of the book) The usual definition of the mean (average) of two numbers \(a\) and \(b\) is \((a+b) / 2\). This is called the arithmetic mean. The geometric mean, however, is defined as \((a b)^{1 / 2}\) (i.e., the square root of \(a b\) ). For the sake of definiteness, let's say both numbers have units of mass. (a) Compute the arithmetic mean of two numbers that have units of grams. Then convert the numbers to units of kilograms and recompute their mean. Is the answer consistent? (b) Do the same for the geometric mean. (c) If \(a\) and \(b\) both have units of grams, what should we call the units of \(a b\) ? Does your answer make sense when you take the square root? (d) Suppose someone proposes to you a third kind of mean, called the superduper mean, defined as \((a b)^{1 / 3}\). Is this reasonable?

Your backyard has brick walls on both ends. You measure a distance of \(23.4 \mathrm{~m}\) from the inside of one wall to the inside of the other. Each wall is \(29.4 \mathrm{~cm}\) thick. How far is it from the outside of one wall to the outside of the other? Pay attention to significant figures.

In Europe, a piece of paper of the standard size, called \(\mathrm{A} 4\), is a little narrower and taller than its American counterpart. The ratio of the height to the width is the square root of 2, and this has some useful properties. For instance, if you cut an A4 sheet from left to right, you get two smaller sheets that have the same proportions. You can even buy sheets of this smaller size, and they're called A5. There is a whole series of sizes related in this way, all with the same proportions. (a) Compare an A5 sheet to an A4 in terms of area and linear size. (b) The series of paper sizes starts from an A0 sheet, which has an area of one square meter. Suppose we had a series of boxes defined in a similar way: the \(\mathrm{B} 0\) box has a volume of one cubic meter, two \(\mathrm{B} 1\) boxes fit exactly inside an \(\mathrm{B} 0 \mathrm{box}\), and so on. What would be the dimensions of a B0 box? (answer check available at lightandmatter.com)

Correct use of a calculator: (a) Calculate \(\frac{74658}{53222+97554}\) on a calculator. [Self-check: The most common mistake results in 97555.40.] (answer check available at lightandmatter.com) (b) Which would be more like the price of a TV, and which would be more like the price of a house, \(\$ 3.5 \times 10^{5}\) or \(\$ 3.5^{5}\) ?

A physics homework question asks, "If you start from rest and accelerate at \(1.54 \mathrm{~m} / \mathrm{s}^{2}\) for \(3.29 \mathrm{~s}\), how far do you travel by the end of that time?" A student answers as follows: $$1.54 \times 3.29-5.07 \mathrm{~m}$$ His Aunt Wanda is good with numbers, but has never taken physics. She doesn't know the formula for the distance traveled under constant acceleration over a given amount of time, but she tells her nephew his answer cannot be right. How does she know?
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