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The steel pipe in (Figure 1) has an inner diameter of 3.41 in and an outer diameter of 3.66 in. If it is fixed at C and subjected to the horizontal 60-lb force acting on the handle of the pipe wrench at its end, determine the principal stresses in the pipe at point A, which is located on the outer surface of the pi

The steel pipe in (Figure 1) has an inner diameter of 3.41 in and an outer diameter of 3.66 in. If it is fixed at C and subjected to the horizontal 60-lb force acting on the handle of the pipe wrench at its end, determine the principal stresses in the pipe at point A, which is located on the outer surface of the pi

Elements Of Electromagnetics
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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The steel pipe in (Figure 1) has an inner diameter of 3.41 in and an outer diameter of 3.66 in.

If it is fixed at C and subjected to the horizontal 60-lb force acting on the handle of the pipe wrench at its end, determine the principal stresses in the pipe at point A, which is located on the outer surface of the pipe.

### Mechanical Advantage and Force Analysis In this diagram, we examine the application of force to a wrench in a mechanical context. This example is useful for understanding concepts such as torque, levers, and force vectors. #### Description of the Diagram - **Wrench and Hand Application:** - A wrench is being used to apply force at a certain point. The user's hand is positioned at the end of the wrench handle. - The handle is parallel to a horizontal plane and makes an angle of 30 degrees with the direction of the applied force. - **Measurements:** - The length of the wrench handle is 12 inches. - The cylindrical shaft to which the wrench is applied is also 12 inches in height. - **Force Application:** - A force of 60 lbs is applied at the end of the wrench handle. - **Reference Points and Axes:** - The point at which the wrench meets the cylindrical shaft is labeled as point \( A \). - There is another point labeled \( B \) near the midpoint on the shaft. - The base of the shaft, resting on a horizontal surface, is labeled as point \( C \). - The diagram uses a three-dimensional coordinate system with the z-axis vertical, y-axis running horizontally to the right, and x-axis extending horizontally out towards the viewer. #### Graphical Analysis - **Force Vector:** - The force of 60 lbs is shown making an angle of 30 degrees downward from the perpendicular to the handle. - **Torque Calculation:** - The torque \( \tau \) applied at point \( A \) can be calculated using the formula \( \tau = r \times F \). - Here, \( r \) is the length of the wrench (12 inches), and \( F \) is the applied force (60 lbs), with consideration of the angle of 30 degrees. #### Educational Outcomes Utilizing this diagram, students can explore the following key mechanical principles: - **Torque and Leverage:** - Understanding how torque is generated and affected by both the length of the lever arm and the angle of force application. - **Vector Decomposition:** - Breaking down the applied force into its components, considering the angle, to better understand how it affects the torque. This visual and practical example aids students in grasping fundamental concepts in physics and engineering related to forces and mechanical advantage.
Transcribed Image Text:### Mechanical Advantage and Force Analysis In this diagram, we examine the application of force to a wrench in a mechanical context. This example is useful for understanding concepts such as torque, levers, and force vectors. #### Description of the Diagram - **Wrench and Hand Application:** - A wrench is being used to apply force at a certain point. The user's hand is positioned at the end of the wrench handle. - The handle is parallel to a horizontal plane and makes an angle of 30 degrees with the direction of the applied force. - **Measurements:** - The length of the wrench handle is 12 inches. - The cylindrical shaft to which the wrench is applied is also 12 inches in height. - **Force Application:** - A force of 60 lbs is applied at the end of the wrench handle. - **Reference Points and Axes:** - The point at which the wrench meets the cylindrical shaft is labeled as point \( A \). - There is another point labeled \( B \) near the midpoint on the shaft. - The base of the shaft, resting on a horizontal surface, is labeled as point \( C \). - The diagram uses a three-dimensional coordinate system with the z-axis vertical, y-axis running horizontally to the right, and x-axis extending horizontally out towards the viewer. #### Graphical Analysis - **Force Vector:** - The force of 60 lbs is shown making an angle of 30 degrees downward from the perpendicular to the handle. - **Torque Calculation:** - The torque \( \tau \) applied at point \( A \) can be calculated using the formula \( \tau = r \times F \). - Here, \( r \) is the length of the wrench (12 inches), and \( F \) is the applied force (60 lbs), with consideration of the angle of 30 degrees. #### Educational Outcomes Utilizing this diagram, students can explore the following key mechanical principles: - **Torque and Leverage:** - Understanding how torque is generated and affected by both the length of the lever arm and the angle of force application. - **Vector Decomposition:** - Breaking down the applied force into its components, considering the angle, to better understand how it affects the torque. This visual and practical example aids students in grasping fundamental concepts in physics and engineering related to forces and mechanical advantage.
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