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Chapter 1: Problem 15

A fathom is a unit of length, usually reserved for measuring the depth of water. A fathom is approximately \(6 \mathrm{ft}\) in length. Take the distance from Earth to the Moon to be 250000 miles, and use the given approximation to find the distance in fathoms.

Short Answer

Expert verified
The distance from Earth to the Moon is approximately 220,000,000 fathoms.

Step by step solution

01

Convert miles to feet

Knowing that 1 mile is approximately 5280 feet, multiply the given distance in miles by 5280. So, if the distance from the Earth to the Moon is 250,000 miles, \(250000 \times 5280 = 1,320,000,000\) feet.
02

Convert feet to fathoms

Knowing that 1 fathom is approximately 6 feet, divide the calculated number of feet by 6. So, \(1,320,000,000 \div 6 = 220,000,000\) fathoms.

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Key Concepts

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

Fathom as a Unit of Length
When it comes to measuring depth, particularly in nautical contexts, the fathom is a traditional unit of length. One fathom is equivalent to approximately 6 feet. This unit has historical roots in sailing and oceanography, where it was originally defined by the span of a man's outstretched arms, which is roughly six feet.

Understanding the fathom is crucial for various reasons, especially in fields such as marine navigation and oceanographic surveys. Even though it is less commonly used today, replaced by metric measurements, the fathom is still employed for certain purposes like determining the depth of water under a ship's keel.
Conversion of Miles to Feet
Converting miles to feet is a fundamental exercise in unit conversion, a crucial skill in physics and everyday life. One mile is officially defined as exactly 5,280 feet. To convert from miles to feet, simply multiply the number of miles by 5,280.

For instance, to convert 10 miles into feet, calculate:
\( 10 \times 5280 = 52,800 \text{ feet} \).

The ability to switch between these units enables precise calculations over a range of disciplines, including engineering, transportation planning, and geographic information systems.
Earth to Moon Distance Measurement
One of the most intriguing astronomical measurements is the distance from the Earth to the Moon. This distance is not only significant for understanding lunar science but also for space exploration efforts. The average distance to the Moon is about 250,000 miles, which can also be expressed in other units like kilometers, feet, or, as in our exercise, fathoms.

This distance to the Moon can be used to demonstrate the principles of unit conversion by converting miles to a smaller unit, such as feet, and then to fathoms. Knowing these concepts and how to apply them to real-world measurements helps students grasp the scale of space and the relevance of unit conversion in science.

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Most popular questions from this chapter

ECP Kinetic energy KE (Chapter 5 ) has dimensions \(\mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\). It can be written in terms of the momentum \(p\) (Chapter 6) and mass m as $$K E=\frac{p^{2}}{2 m}$$ (a) Determine the proper units for momentum using dimensional analysis. (b) Refer to Problem 5, Given the units of force, write a simple equation relating a constant force \(F\) exerted on an object, an interval of time \(t\) during which the force is applied, and the resulting momentum of the object, \(p\).

The speed of light is about \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Convert this figure to miles per hour.

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The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by $$T=2 \pi \sqrt{\frac{\ell}{g}}$$ where \(\ell\) is the length of the pendulum and \(g\) is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. (You might want to check the formula using your keys at the end of a string and a stopwatch.)

(a) One of the fundamental laws of motion states that the acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (b) The newton is the SI unit of force. According to the results for (a), how can you express a force having units of newtons by using the fundamental units of mass, length, and time?
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