Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Problem Statement:**
Find the work done for a force \( F = \frac{12}{x^2} \) N when moving an object from \( x = 2 \) m to \( x = 6 \) m.
**Explanation:**
This problem involves calculating the work done by a variable force over a distance. Here, the force \( F \) is given as a function of distance \( x \):
\[ F(x) = \frac{12}{x^2} \]
To find the work done, we need to integrate this force function over the given limits from \( x = 2 \) meters to \( x = 6 \) meters. The work done \( W \) is given by the integral:
\[ W = \int_{2}^{6} F(x) \, dx = \int_{2}^{6} \frac{12}{x^2} \, dx \]
**Purpose:**
This example illustrates how to apply the concept of integration in physics to determine work done by a variable force.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F678fef96-64be-4096-a74a-c4eb0a405ee7%2Ff31181de-ca4f-4850-9a97-21801ce9da85%2Fkfjdamg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the work done for a force \( F = \frac{12}{x^2} \) N when moving an object from \( x = 2 \) m to \( x = 6 \) m.
**Explanation:**
This problem involves calculating the work done by a variable force over a distance. Here, the force \( F \) is given as a function of distance \( x \):
\[ F(x) = \frac{12}{x^2} \]
To find the work done, we need to integrate this force function over the given limits from \( x = 2 \) meters to \( x = 6 \) meters. The work done \( W \) is given by the integral:
\[ W = \int_{2}^{6} F(x) \, dx = \int_{2}^{6} \frac{12}{x^2} \, dx \]
**Purpose:**
This example illustrates how to apply the concept of integration in physics to determine work done by a variable force.
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