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The 50-lb mulching machine has a center of gravity at G. Determine the vertical reactions at the wheels C and B and the smooth contact point A. 4 ft 1.25 ft 1.25 ft

The 50-lb mulching machine has a center of gravity at G. Determine the vertical reactions at the wheels C and B and the smooth contact point A. 4 ft 1.25 ft 1.25 ft

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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**Problem Statement:** The 50-lb mulching machine has a center of gravity at \( G \). Determine the vertical reactions at the wheels \( C \) and \( B \) and the smooth contact point \( A \). **Diagram Explanation:** The diagram illustrates a mulching machine positioned on a sloped surface. The machine's center of gravity \( G \) is located above point \( B \). - The \( x, y, z \) coordinate system is shown with the origin at point \( A \). - The machine has three points of interest: - **Point \( A \)**: Located at the left and in contact with the surface. - **Point \( B \)**: Positioned on the ground, aligned with a wheel. - **Point \( C \)**: The third point of contact with the surface to the right. **Distances:** - From \( A \) to \( B \): 1.5 ft along the \( x \)-axis and 2 ft along the \( y \)-axis. - From \( B \) to \( C \): 1.25 ft along the \( y \)-axis. - The center of gravity \( G \) is located 4 ft above point \( C \). Two arrows below the machine indicate forces acting upward, likely representing the reactions at points \( B \) and \( C \). These forces are parallel to the \( z \)-axis. Use the given distances to set up equations for equilibrium to determine the vertical reactions at points \( A \), \( B \), and \( C \).
Transcribed Image Text:**Problem Statement:** The 50-lb mulching machine has a center of gravity at \( G \). Determine the vertical reactions at the wheels \( C \) and \( B \) and the smooth contact point \( A \). **Diagram Explanation:** The diagram illustrates a mulching machine positioned on a sloped surface. The machine's center of gravity \( G \) is located above point \( B \). - The \( x, y, z \) coordinate system is shown with the origin at point \( A \). - The machine has three points of interest: - **Point \( A \)**: Located at the left and in contact with the surface. - **Point \( B \)**: Positioned on the ground, aligned with a wheel. - **Point \( C \)**: The third point of contact with the surface to the right. **Distances:** - From \( A \) to \( B \): 1.5 ft along the \( x \)-axis and 2 ft along the \( y \)-axis. - From \( B \) to \( C \): 1.25 ft along the \( y \)-axis. - The center of gravity \( G \) is located 4 ft above point \( C \). Two arrows below the machine indicate forces acting upward, likely representing the reactions at points \( B \) and \( C \). These forces are parallel to the \( z \)-axis. Use the given distances to set up equations for equilibrium to determine the vertical reactions at points \( A \), \( B \), and \( C \).
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