**Problem 6.20 - Enhanced - with Feedback****Part A**A wind turbine has \( 12,000 \, \text{kg} \) blades that are \( 41 \, \text{m} \) long. The blades spin at \( 24 \, \text{rpm} \).---In this section, we will analyze the properties and dynamics of the wind turbine blades. The turbines under examination have significant mass and length, making their rotational characteristics and the forces acting upon them crucial for understanding their operation and performance.1. Blade Mass: \( 12,000 \, \text{kg} \)2. Blade Length: \( 41 \, \text{m} \)3. Rotation Speed: \( 24 \, \text{rpm} \) (revolutions per minute) ### Educational Resource: Understanding Centripetal Force#### Part A**Problem Statement:**If we model a blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each blade's centripetal acceleration?**Instructions for Students:**Express your answer with the appropriate units.**Answer Format:**\[ F = \text{Value} \: \text{Units} \]**Input Tools:**- **Square Root Button (√)**- **Square Button (x²)**- **Unit Selector**- **Clear Button (↻)**- **Help Button (?)****Explanation:**This problem requires students to calculate the inward (centripetal) force needed to keep a blade, modeled as a point mass at its midpoint, in circular motion. The centripetal force is necessary to provide the required centripetal acceleration, keeping the blade moving in a circular path.When answering, make sure to:1. Calculate the value of the centripetal force using the given parameters.2. Use the correct units to express your force value.**Formula Reminder:**The centripetal force \( F \) can be calculated using the formula:\[ F = m \cdot a_c \]where \( m \) = mass of the point (blade),\( a_c \) = centripetal acceleration.For reference, centripetal acceleration \( a_c \) is given by:\[ a_c = \frac{v^2}{r} \]where \( v \) = velocity,\( r \) = radius of the circular path.Or alternatively:\[ a_c = r \cdot \omega^2 \]where \( \omega \) = angular velocity.Students should verify their units and ensure that the calculation matches the physical context of the problem.

Answered: Image /qna-images/answer/4ea8646e-ff1d-4ab3-88f7-bd059a0b6259.jpg

Answered: Problem 6.20 - Enhanced - with Feedback…

Problem 6.20 - Enhanced - with Feedback A wind turbine has 12,000 kg blades that are 41 m long. The blades spin at 24 rpm. Part A If we model a blade as a point mass at

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 33PQ: Consider again the two wind turbines in Problem 32. a. At what point along the 40-m blade would the...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Problem 6.20 - Enhanced - with Feedback**

**Part A**

A wind turbine has \( 12,000 \, \text{kg} \) blades that are \( 41 \, \text{m} \) long. The blades spin at \( 24 \, \text{rpm} \).

---

In this section, we will analyze the properties and dynamics of the wind turbine blades. The turbines under examination have significant mass and length, making their rotational characteristics and the forces acting upon them crucial for understanding their operation and performance.

1. Blade Mass: \( 12,000 \, \text{kg} \)
2. Blade Length: \( 41 \, \text{m} \)
3. Rotation Speed: \( 24 \, \text{rpm} \) (revolutions per minute)

### Educational Resource: Understanding Centripetal Force

#### Part A

**Problem Statement:**
If we model a blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each blade's centripetal acceleration?

**Instructions for Students:**
Express your answer with the appropriate units.

**Answer Format:**
\[ F = \text{Value} \: \text{Units} \]

**Input Tools:**
- **Square Root Button (√)**
- **Square Button (x²)**
- **Unit Selector**
- **Clear Button (↻)**
- **Help Button (?)**

**Explanation:**
This problem requires students to calculate the inward (centripetal) force needed to keep a blade, modeled as a point mass at its midpoint, in circular motion. The centripetal force is necessary to provide the required centripetal acceleration, keeping the blade moving in a circular path.

When answering, make sure to:
1. Calculate the value of the centripetal force using the given parameters.
2. Use the correct units to express your force value.

**Formula Reminder:**
The centripetal force \( F \) can be calculated using the formula:
\[ F = m \cdot a_c \]
where
\( m \) = mass of the point (blade),
\( a_c \) = centripetal acceleration.

For reference, centripetal acceleration \( a_c \) is given by:
\[ a_c = \frac{v^2}{r} \]
where
\( v \) = velocity,
\( r \) = radius of the circular path.

Or alternatively:
\[ a_c = r \cdot \omega^2 \]
where
\( \omega \) = angular velocity.

Students should verify their units and ensure that the calculation matches the physical context of the problem.

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