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
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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
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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