A heavy crate is dragged 70 feet along a level floor. Find the work done if a force of 20 pounds at an angle of 32° is used. Round your answer to the nearest tenth. 989.3 ft-lb 874.8 ft-lb 741.9 ft-lb 1,187.3 ft-lb E
A heavy crate is dragged 70 feet along a level floor. Find the work done if a force of 20 pounds at an angle of 32° is used. Round your answer to the nearest tenth. 989.3 ft-lb 874.8 ft-lb 741.9 ft-lb 1,187.3 ft-lb E
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 28CT: Force Tyler and his cousin Kelly have attached a rope to the branch of a tree and tied a board to...
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Question
![### Work Done by a Force: Educational Example
**Problem Statement:**
A heavy crate is dragged 70 feet along a level floor. Find the work done if a force of 20 pounds at an angle of 32° is used. Round your answer to the nearest tenth.
**Options:**
1. 989.3 ft·lb
2. 874.8 ft·lb
3. 741.9 ft·lb
4. 1,187.3 ft·lb
**Explanation:**
To solve this problem, we need to calculate the work done using the formula:
\[ \text{Work} = F \cdot d \cdot \cos(\theta) \]
Where:
- \( F \) is the force applied (20 pounds)
- \( d \) is the distance over which the force is applied (70 feet)
- \( \theta \) is the angle of the force with respect to the horizontal (32°)
- \( \cos \) is the cosine function, which can be calculated using a calculator.
### Step-by-Step Calculation:
1. **Calculate \( \cos(32^\circ) \):**
\[
\cos(32^\circ) \approx 0.848
\]
2. **Substitute the known values into the work formula:**
\[
\text{Work} = 20 \, \text{lb} \cdot 70 \, \text{ft} \cdot 0.848
\]
3. **Compute the product:**
\[
\text{Work} \approx 20 \cdot 70 \cdot 0.848 = 1,187.2 \, \text{ft}\cdot\text{lb}
\]
4. **Round the result to the nearest tenth:**
\[
\text{Work} \approx 1,187.2 \, \text{ft}\cdot\text{lb}
\]
Rounded to the nearest tenth, the work done is:
\[
\boxed{1,187.3 \, \text{ft}\cdot\text{lb}}
\]
**Correct Answer:**
4. 1,187.3 ft·lb](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc5bcc65-7283-4529-b9b7-ffbb90a5afc1%2F30ab81a0-0549-40f1-829e-6020a5553697%2Fv02xxz9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Work Done by a Force: Educational Example
**Problem Statement:**
A heavy crate is dragged 70 feet along a level floor. Find the work done if a force of 20 pounds at an angle of 32° is used. Round your answer to the nearest tenth.
**Options:**
1. 989.3 ft·lb
2. 874.8 ft·lb
3. 741.9 ft·lb
4. 1,187.3 ft·lb
**Explanation:**
To solve this problem, we need to calculate the work done using the formula:
\[ \text{Work} = F \cdot d \cdot \cos(\theta) \]
Where:
- \( F \) is the force applied (20 pounds)
- \( d \) is the distance over which the force is applied (70 feet)
- \( \theta \) is the angle of the force with respect to the horizontal (32°)
- \( \cos \) is the cosine function, which can be calculated using a calculator.
### Step-by-Step Calculation:
1. **Calculate \( \cos(32^\circ) \):**
\[
\cos(32^\circ) \approx 0.848
\]
2. **Substitute the known values into the work formula:**
\[
\text{Work} = 20 \, \text{lb} \cdot 70 \, \text{ft} \cdot 0.848
\]
3. **Compute the product:**
\[
\text{Work} \approx 20 \cdot 70 \cdot 0.848 = 1,187.2 \, \text{ft}\cdot\text{lb}
\]
4. **Round the result to the nearest tenth:**
\[
\text{Work} \approx 1,187.2 \, \text{ft}\cdot\text{lb}
\]
Rounded to the nearest tenth, the work done is:
\[
\boxed{1,187.3 \, \text{ft}\cdot\text{lb}}
\]
**Correct Answer:**
4. 1,187.3 ft·lb
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