At the instant θ=60∘, the construction lift is rotating about the z axis with an angular velocity of ω1 = 0.55 rad/s and an angular acceleration of ω˙1 = 0.21 rad/s2 while the telescopic boom AB rotates about the pin at A with an angular velocity of ω2 = 0.21 rad/s and angular acceleration of ω˙2 = 6.0×10−2 rad/s2 . Simultaneously, the boom is extending with a velocity of 1.5 ft / s, and it has an acceleration of 0.5 ft / s2, both measured relative to the frame. Determine the velocity of point B located at the end of the boom at this instant. Enter the x, y, and z components of the velocity separated by commas. Determine the acceleration of point B located at the end of the boom at this instant. Enter the x, y, and z components of the acceleration separated by commas. This diagram illustrates a boom lift mechanism with several key components and notations for educational purposes.### Components:- **Platform B:** The upper-most point of the boom, marked at a height of 15 ft from the pivot point A.- **Boom Arm:** A structure enabling the platform to extend and elevate. The angle of elevation from the horizontal is denoted by \( \theta \).- **Pivot Point A:** The location where the boom arm is attached to the base, allowing rotation.- **Base:** The vehicular platform that houses the pivot and provides mobility. The distance from the pivot point A to the edge C is 2 ft.### Axes and Rotational Notations:- **Coordinate Axes:** - **x-axis:** Extends horizontally, parallel to the ground. - **y-axis:** Extends horizontally, perpendicular to the x-axis, lying in the plane of the diagram. - **z-axis:** Extends vertically upwards from the ground.- **Angular Velocities:** - \( \omega_1 \) and \( \dot{\omega}_1 \) are depicted as rotational arrows around the z-axis, indicating the angular velocity and its time derivative of rotation about the vertical axis. - \( \omega_2 \) and \( \dot{\omega}_2 \) are depicted as rotational arrows around the x-axis, indicating the angular velocity and its time derivative of the tilt or elevation angle \( \theta \).This setup is often used in physics and engineering to demonstrate rotational mechanics, balance, and stability of construction equipment under different operational circumstances.

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Answered: At the instant θ=60∘, the construction…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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At the instant θ=60∘, the construction lift is rotating about the z axis with an angular velocity of ω1 = 0.55 rad/s and an angular acceleration of ω˙1 = 0.21 rad/s2 while the telescopic boom AB rotates about the pin at A with an angular velocity of ω2 = 0.21 rad/s and angular acceleration of ω˙2 = 6.0×10−2 rad/s2 . Simultaneously, the boom is extending with a velocity of 1.5 ft / s, and it has an acceleration of 0.5 ft / s2, both measured relative to the frame.

Determine the velocity of point B located at the end of the boom at this instant. Enter the x, y, and z components of the velocity separated by commas.

Determine the acceleration of point B located at the end of the boom at this instant. Enter the x, y, and z components of the acceleration separated by commas.

This diagram illustrates a boom lift mechanism with several key components and notations for educational purposes.

### Components:
- **Platform B:** The upper-most point of the boom, marked at a height of 15 ft from the pivot point A.
- **Boom Arm:** A structure enabling the platform to extend and elevate. The angle of elevation from the horizontal is denoted by \( \theta \).
- **Pivot Point A:** The location where the boom arm is attached to the base, allowing rotation.
- **Base:** The vehicular platform that houses the pivot and provides mobility. The distance from the pivot point A to the edge C is 2 ft.

### Axes and Rotational Notations:
- **Coordinate Axes:**
- **x-axis:** Extends horizontally, parallel to the ground.
- **y-axis:** Extends horizontally, perpendicular to the x-axis, lying in the plane of the diagram.
- **z-axis:** Extends vertically upwards from the ground.

- **Angular Velocities:**
- \( \omega_1 \) and \( \dot{\omega}_1 \) are depicted as rotational arrows around the z-axis, indicating the angular velocity and its time derivative of rotation about the vertical axis.
- \( \omega_2 \) and \( \dot{\omega}_2 \) are depicted as rotational arrows around the x-axis, indicating the angular velocity and its time derivative of the tilt or elevation angle \( \theta \).

This setup is often used in physics and engineering to demonstrate rotational mechanics, balance, and stability of construction equipment under different operational circumstances.

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