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Chapter 1: Problem 38

The British Gravitational System uses the mass unit slug. By definition, a mass of 1 slug is accelerated at a rate of \(1 \mathrm{ft} / \mathrm{s}^{2}\) by a force of \(1 \mathrm{lb}\). Explain why this is a convenient mass unit.

Short Answer

Expert verified
The slug is a convenient unit of mass in the British Gravitational System because it simplifies the calculation of force. If an object with a mass of 1 slug is subject to an acceleration of \(1 \mathrm{ft}/\mathrm{s}^2\), it produces a force of 1 lb. This way, the unit slug allows for easy and direct measurement of force in everyday scenarios, making complex physics concepts more relatable and understandable.

Step by step solution

01

Understand Basic Definitions and Relations

Firstly, it is crucial to comprehend that according to Newton's second law, the force \( F \) is the product of an object's mass \( m \) and its acceleration \( a \). This can be written in the form, \( F = m \cdot a \). When the mass is 1 slug and the acceleration is \(1 \mathrm{ft}/\mathrm{s}^2\), the resulting force, by definition, is 1 pound force or lb.
02

Discuss the Convenience

As seen from the above equation, using slug as a unit of mass results in a simple and direct measurement of force in pounds. When the acceleration is \(1 \mathrm{ft}/\mathrm{s}^2\), 1 slug of mass directly equates to 1 pound of force. This makes the calculations simpler and easier compared to other systems. It also allows for easy conceptualization, as these units have tangible representations in daily life, making it easier to grasp physics concepts.

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