t 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 comm

Elements Of Electromagnetics
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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 comm

 

Determine the acceleration of point BB located at the end of the boom at this instant.
 

 

This illustration depicts a mobile articulating boom lift, a type of aerial work platform. The diagram includes several key components and measurements important for understanding the machine’s operation:

1. **Boom Structure**: The boom is shown extending at an angle \( \theta \) from the base. It consists of two connected segments, with point \( A \) acting as a pivot point for the dual arms.

2. **Rotational Axes and Angles**:
   - \( \omega_1 \) and \( \dot{\omega_1} \) represent rotational motion about the vertical z-axis, at a point 15 feet from the base where the basket is located.
   - \( \omega_2 \) and \( \dot{\omega_2} \) denote rotational motion about the horizontal x-axis, located at a distance of 2 feet from the center of the base at point \( O \).

3. **Key Points and Distances**:
   - Point \( B \) is at the upper end of the boom where the platform is situated.
   - Distances are marked from the origin (\( O \)) to significant points, with 15 ft along the boom to point \( B \) and 2 ft vertically to point \( A \).

4. **Coordinate Axes**: 
   - The z-axis is vertical, aligned with the upright orientation of the lift.
   - The x and y axes denote the horizontal plane, perpendicular to each other.

This setup allows for comprehensive motion analysis of the boom lift, which is critical for tasks such as determining the stability, reach, and operational safety in varying conditions.
Transcribed Image Text:This illustration depicts a mobile articulating boom lift, a type of aerial work platform. The diagram includes several key components and measurements important for understanding the machine’s operation: 1. **Boom Structure**: The boom is shown extending at an angle \( \theta \) from the base. It consists of two connected segments, with point \( A \) acting as a pivot point for the dual arms. 2. **Rotational Axes and Angles**: - \( \omega_1 \) and \( \dot{\omega_1} \) represent rotational motion about the vertical z-axis, at a point 15 feet from the base where the basket is located. - \( \omega_2 \) and \( \dot{\omega_2} \) denote rotational motion about the horizontal x-axis, located at a distance of 2 feet from the center of the base at point \( O \). 3. **Key Points and Distances**: - Point \( B \) is at the upper end of the boom where the platform is situated. - Distances are marked from the origin (\( O \)) to significant points, with 15 ft along the boom to point \( B \) and 2 ft vertically to point \( A \). 4. **Coordinate Axes**: - The z-axis is vertical, aligned with the upright orientation of the lift. - The x and y axes denote the horizontal plane, perpendicular to each other. This setup allows for comprehensive motion analysis of the boom lift, which is critical for tasks such as determining the stability, reach, and operational safety in varying conditions.
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