Work The force F = 4i – 7j moves an object 4 ft along the x-axis in the positive direction. Find the work done if the unit of force is the pound.
Work The force F = 4i – 7j moves an object 4 ft along the x-axis in the positive direction. Find the work done if the unit of force is the pound.
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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![**Problem**: The force \(\mathbf{F} = 4\mathbf{i} - 7\mathbf{j}\) moves an object 4 ft along the x-axis in the positive direction. Find the work done if the unit of force is the pound.
**Solution**:
1. **Identify the Given Force**:
\(\mathbf{F} = 4\mathbf{i} - 7\mathbf{j}\)
2. **Direction of Motion**:
The object moves 4 feet along the x-axis in the positive direction.
3. **Calculate the Work Done**:
Work done is calculated using the dot product of force and displacement. The displacement vector is \(\mathbf{d} = 4\mathbf{i}\).
\[
\text{Work} = \mathbf{F} \cdot \mathbf{d} = (4\mathbf{i} - 7\mathbf{j}) \cdot 4\mathbf{i}
\]
\[
= 4 \cdot 4 + (-7) \cdot 0
\]
\[
= 16 \, \text{foot-pounds}
\]
Thus, the work done is 16 foot-pounds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4248fea-c75e-4e96-a274-f1cd3c8da07a%2Fafea3585-8ce1-414c-a953-c6330b42c76a%2F5m55tdhj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem**: The force \(\mathbf{F} = 4\mathbf{i} - 7\mathbf{j}\) moves an object 4 ft along the x-axis in the positive direction. Find the work done if the unit of force is the pound.
**Solution**:
1. **Identify the Given Force**:
\(\mathbf{F} = 4\mathbf{i} - 7\mathbf{j}\)
2. **Direction of Motion**:
The object moves 4 feet along the x-axis in the positive direction.
3. **Calculate the Work Done**:
Work done is calculated using the dot product of force and displacement. The displacement vector is \(\mathbf{d} = 4\mathbf{i}\).
\[
\text{Work} = \mathbf{F} \cdot \mathbf{d} = (4\mathbf{i} - 7\mathbf{j}) \cdot 4\mathbf{i}
\]
\[
= 4 \cdot 4 + (-7) \cdot 0
\]
\[
= 16 \, \text{foot-pounds}
\]
Thus, the work done is 16 foot-pounds.
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