The handle of a vegetable wagon makes an angle of 35.0° with the horizontal. If the peddler exerts a force of 35.0 lb along the handle, how much work (in joules) does the peddler do in pulling the cart 1.20 mi?
The handle of a vegetable wagon makes an angle of 35.0° with the horizontal. If the peddler exerts a force of 35.0 lb along the handle, how much work (in joules) does the peddler do in pulling the cart 1.20 mi?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem Statement
**Question 2:** The handle of a vegetable wagon makes an angle of 35.0° with the horizontal. If the peddler exerts a force of 35.0 lb along the handle, how much work (in joules) does the peddler do in pulling the cart 1.20 mi?
### Solution
To solve this problem, we need to calculate the work done by the peddler. Work is given by the formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
Where:
- Force (F) is 35.0 lb.
- Distance (d) is 1.20 mi.
- Angle (\(\theta\)) is 35.0°.
First, convert the units to be consistent (feet for distance and pounds for force), and then use appropriate conversions to obtain the final answer in joules.
1. **Convert Distance:**
\[
1 \text{ mile} = 5280 \text{ feet}
\]
\[
\text{Distance} = 1.20 \text{ mi} \times 5280 \text{ ft/mi} = 6336 \text{ ft}
\]
2. **Calculate Work in Foot-Pounds:**
\[
\text{Work} = 35.0 \text{ lb} \times 6336 \text{ ft} \times \cos(35.0^\circ)
\]
\[
\cos(35.0^\circ) \approx 0.8192
\]
\[
\text{Work} = 35.0 \times 6336 \times 0.8192 \approx 182,095.872 \text{ ft-lb}
\]
3. **Convert Foot-Pounds to Joules:**
\[
1 \text{ ft-lb} = 1.35582 \text{ J}
\]
\[
\text{Work in Joules} = 182,095.872 \text{ ft-lb} \times 1.35582 \text{ J/ft-lb} \approx 246,793.81 \text{ J}
\]
### Final Answer
The amount of work done](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb81255bd-f398-4040-92a3-0b816125fc2f%2F79cddc44-e94c-47e5-9829-a7a7779cb06a%2Fdg6o4wa_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Question 2:** The handle of a vegetable wagon makes an angle of 35.0° with the horizontal. If the peddler exerts a force of 35.0 lb along the handle, how much work (in joules) does the peddler do in pulling the cart 1.20 mi?
### Solution
To solve this problem, we need to calculate the work done by the peddler. Work is given by the formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
Where:
- Force (F) is 35.0 lb.
- Distance (d) is 1.20 mi.
- Angle (\(\theta\)) is 35.0°.
First, convert the units to be consistent (feet for distance and pounds for force), and then use appropriate conversions to obtain the final answer in joules.
1. **Convert Distance:**
\[
1 \text{ mile} = 5280 \text{ feet}
\]
\[
\text{Distance} = 1.20 \text{ mi} \times 5280 \text{ ft/mi} = 6336 \text{ ft}
\]
2. **Calculate Work in Foot-Pounds:**
\[
\text{Work} = 35.0 \text{ lb} \times 6336 \text{ ft} \times \cos(35.0^\circ)
\]
\[
\cos(35.0^\circ) \approx 0.8192
\]
\[
\text{Work} = 35.0 \times 6336 \times 0.8192 \approx 182,095.872 \text{ ft-lb}
\]
3. **Convert Foot-Pounds to Joules:**
\[
1 \text{ ft-lb} = 1.35582 \text{ J}
\]
\[
\text{Work in Joules} = 182,095.872 \text{ ft-lb} \times 1.35582 \text{ J/ft-lb} \approx 246,793.81 \text{ J}
\]
### Final Answer
The amount of work done
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