For a short time the bucket of the backhoe traces the path of the cardioid r= 25(1- cos 0) ft. The boom is rotating with an angular velocity of å = 1.8 rad/s and an angular acceleration of = 0.17 rad/s at the instant shown. e- 120 Part A Determine the magnitude of the velooity of the bucket when 0- 120. Express your answer to three significant figures and include the appropriate units. You did not open hints for this par. Part B Determine the magnitude of the acceleration of the bucket when = 120°. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part
For a short time the bucket of the backhoe traces the path of the cardioid r= 25(1- cos 0) ft. The boom is rotating with an angular velocity of å = 1.8 rad/s and an angular acceleration of = 0.17 rad/s at the instant shown. e- 120 Part A Determine the magnitude of the velooity of the bucket when 0- 120. Express your answer to three significant figures and include the appropriate units. You did not open hints for this par. Part B Determine the magnitude of the acceleration of the bucket when = 120°. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![### Determining Velocity and Acceleration for a Backhoe Bucket
For a short time, the bucket of the backhoe traces the path of the cardioid given by the equation\[ r = 25 (1 - \cos(\theta)) \] feet. The boom is rotating with an angular velocity of \[ \dot{\theta} = 1.8 \text{ rad/s} \] and an angular acceleration of \[ \ddot{\theta} = 0.17 \text{ rad/s}^2 \] at the instant shown in the image. In the figure, the backhoe's boom traces this path with an angle \( \theta = 120^\circ \).
#### Diagram Explanation
The diagram features an image of a backhoe loader with its boom extended to trace a cardioid path in the air. The bucket is positioned such that the angle \( \theta \) between the boom and the ground is \( 120^\circ \). This configuration represents the angle at which the calculations of velocity and acceleration should be determined.
### Part A
#### Calculating the Magnitude of Velocity
Determine the magnitude of the velocity of the bucket when \( \theta = 120^\circ \).
**Instructions:** Express your answer to three significant figures and include the appropriate units.
\[ v = \]
(Note: No hints were provided for this part.)
### Part B
#### Calculating the Magnitude of Acceleration
Determine the magnitude of the acceleration of the bucket when \( \theta = 120^\circ \).
**Instructions:** Express your answer to three significant figures and include the appropriate units.
\[ a = \]
(Note: No hints were provided for this part.)
This educational exercise helps to understand the motion dynamics of mechanical parts in engineering using trigonometric and calculus concepts in a practical application. The analysis of velocity and acceleration at a specific point (\( \theta = 120^\circ \)) provides insight into the kinematic behavior of the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f88d8b4-ac68-457e-9d02-d311a9616c7b%2F63f23c6e-7dc5-4f7e-b214-041adc4ab0c1%2Fybczpr_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining Velocity and Acceleration for a Backhoe Bucket
For a short time, the bucket of the backhoe traces the path of the cardioid given by the equation\[ r = 25 (1 - \cos(\theta)) \] feet. The boom is rotating with an angular velocity of \[ \dot{\theta} = 1.8 \text{ rad/s} \] and an angular acceleration of \[ \ddot{\theta} = 0.17 \text{ rad/s}^2 \] at the instant shown in the image. In the figure, the backhoe's boom traces this path with an angle \( \theta = 120^\circ \).
#### Diagram Explanation
The diagram features an image of a backhoe loader with its boom extended to trace a cardioid path in the air. The bucket is positioned such that the angle \( \theta \) between the boom and the ground is \( 120^\circ \). This configuration represents the angle at which the calculations of velocity and acceleration should be determined.
### Part A
#### Calculating the Magnitude of Velocity
Determine the magnitude of the velocity of the bucket when \( \theta = 120^\circ \).
**Instructions:** Express your answer to three significant figures and include the appropriate units.
\[ v = \]
(Note: No hints were provided for this part.)
### Part B
#### Calculating the Magnitude of Acceleration
Determine the magnitude of the acceleration of the bucket when \( \theta = 120^\circ \).
**Instructions:** Express your answer to three significant figures and include the appropriate units.
\[ a = \]
(Note: No hints were provided for this part.)
This educational exercise helps to understand the motion dynamics of mechanical parts in engineering using trigonometric and calculus concepts in a practical application. The analysis of velocity and acceleration at a specific point (\( \theta = 120^\circ \)) provides insight into the kinematic behavior of the system.
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