**Oil Pumping Unit Dynamics***Problem Statement:*The oil pumping unit consists of a walking beam \( AB \), a connecting rod \( BC \), and a crank \( CD \). The system operates with the crank rotating at a constant \( 6 \, \text{rad/s} \). The objective is to determine the speed of the rod hanger \( H \) at the specific instant depicted in the diagram. Note that point \( B \) traces a circular path about point \( E \), implying that the velocity of \( B \) is not purely vertical.*Steps for Analysis:*1. Clearly indicate the instantaneous center (IC) of \( BC \) and \( AB \).2. Determine: - Angular velocities of \( BC \) and \( AB \). - Speeds and directions of points \( C \), \( B \), and \( A \).*Diagram Explanation:*The diagram illustrates an oil pumping unit with the following dimensions and components:- A crank \( CD \) rotating at \( 6 \, \text{rad/s} \).- The length of the walking beam \( AB \) is \( 9 \, \text{ft} \).- The beam is divided into equal segments, each \( 9 \, \text{ft} \) long, forming a right triangle with a vertical \( 3 \, \text{ft} \) offset at point \( B \).- The point \( H \), where the speed is to be calculated, is located at one end of the beam.This setup models the kinematic behavior of the oil pumping unit, utilizing geometric relationships and rotational dynamics to determine velocities within the system.

Given: To find: Velocity of rod hanger H

The oil pumping unit consists of a walking beam AB, a connecting rod BC, and crank CD. If the crank rotates at a constant 6 rad/s, find the speed of the rod hanger H at the instant shown. Hint, the point B follows a circular path about point E and therefore the velocity of B is not vertical. To communicate, make review meaningful, clearly show the IC of BC and AB ●. ● ● angular velocities of BC and AB speeds and directions of C, B, and A.

The oil pumping unit consists of a walking beam AB, a connecting rod BC, and crank CD. If the crank rotates at a constant 6 rad/s, find the speed of the rod hanger H at the instant shown. Hint, the point B follows a circular path about point E and therefore the velocity of B is not vertical. To communicate, make review meaningful, clearly show the IC of BC and AB ●. ● ● angular velocities of BC and AB speeds and directions of C, B, and A.

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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Question

**Oil Pumping Unit Dynamics**

*Problem Statement:*

The oil pumping unit consists of a walking beam \( AB \), a connecting rod \( BC \), and a crank \( CD \). The system operates with the crank rotating at a constant \( 6 \, \text{rad/s} \). The objective is to determine the speed of the rod hanger \( H \) at the specific instant depicted in the diagram. Note that point \( B \) traces a circular path about point \( E \), implying that the velocity of \( B \) is not purely vertical.

*Steps for Analysis:*

1. Clearly indicate the instantaneous center (IC) of \( BC \) and \( AB \).

2. Determine:
- Angular velocities of \( BC \) and \( AB \).
- Speeds and directions of points \( C \), \( B \), and \( A \).

*Diagram Explanation:*

The diagram illustrates an oil pumping unit with the following dimensions and components:
- A crank \( CD \) rotating at \( 6 \, \text{rad/s} \).
- The length of the walking beam \( AB \) is \( 9 \, \text{ft} \).
- The beam is divided into equal segments, each \( 9 \, \text{ft} \) long, forming a right triangle with a vertical \( 3 \, \text{ft} \) offset at point \( B \).
- The point \( H \), where the speed is to be calculated, is located at one end of the beam.

This setup models the kinematic behavior of the oil pumping unit, utilizing geometric relationships and rotational dynamics to determine velocities within the system.

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