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The force of F = 85 lb acts along the edge DB of the tetrahedron shown in (Figure 1). Figure < 1 of 1 > Part A Determine the magnitude of the moment of this force about the edge CA Express your answer in pound-feet to three significant figures. MAC = Submit AEO Request Answer vec ? lb-ft

The force of F = 85 lb acts along the edge DB of the tetrahedron shown in (Figure 1). Figure < 1 of 1 > Part A Determine the magnitude of the moment of this force about the edge CA Express your answer in pound-feet to three significant figures. MAC = Submit AEO Request Answer vec ? lb-ft

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### Tetrahedron Mechanics Problem **Problem Statement:** The force \( F = 85 \) lb acts along the edge \( DB \) of the tetrahedron shown in the figure below. **Figure 1:** The figure depicts a tetrahedron with vertices labeled as \( A \), \( B \), \( C \), and \( D \). The structure is positioned in a 3-dimensional coordinate system with coordinates as follows: - Vertex \( A \): designated as the origin. - Vertex \( B \): located at \( (10 \text{ ft}, 0, 0) \). - Vertex \( C \): positioned at \( (4 \text{ ft}, 6 \text{ ft}, 0) \). - Vertex \( D \): positioned at \( (0, 0, 15\text{ ft}) \). The force vector \( \mathbf{F} \) is shown along the edge \( DB \). **Part A:** Determine the magnitude of the moment of this force about the edge \( CA \). **Instructions:** Express your answer in pound-feet to three significant figures. \[ M_{AC} = \] **(Input box for the answer: lb \cdot ft)** **Please refer to the diagram in Figure 1 for spatial orientation and measurements.** #### Diagram Explanation: - The tetrahedron is situated in 3D space with the following dimensions: - Distance \( AB = 10 \) ft - Distance \( AC = 8 \) ft - Distance \( AD = 15 \) ft - The base lies along the \( xy \)-plane. - Axes: - \( x \)-axis aligns with \( A \to B \) - \( y \)-axis runs perpendicular from \( A \) in the \( xy \)-plane to \( C \) - \( z \)-axis is vertical, leading from \( A \) to \( D \) Use the provided axes and coordinates to determine the solution accurately. **Submit Answer Button:** After computing the required moment, insert the value into the input box and click ‘Submit’. **Provide Feedback Link:** Click here if you have any feedback regarding this problem. --- **Note:** When solving for moments in 3D problems, consider using vector cross product formulas and the position vectors of the points involved to ensure precision.
Transcribed Image Text:### Tetrahedron Mechanics Problem **Problem Statement:** The force \( F = 85 \) lb acts along the edge \( DB \) of the tetrahedron shown in the figure below. **Figure 1:** The figure depicts a tetrahedron with vertices labeled as \( A \), \( B \), \( C \), and \( D \). The structure is positioned in a 3-dimensional coordinate system with coordinates as follows: - Vertex \( A \): designated as the origin. - Vertex \( B \): located at \( (10 \text{ ft}, 0, 0) \). - Vertex \( C \): positioned at \( (4 \text{ ft}, 6 \text{ ft}, 0) \). - Vertex \( D \): positioned at \( (0, 0, 15\text{ ft}) \). The force vector \( \mathbf{F} \) is shown along the edge \( DB \). **Part A:** Determine the magnitude of the moment of this force about the edge \( CA \). **Instructions:** Express your answer in pound-feet to three significant figures. \[ M_{AC} = \] **(Input box for the answer: lb \cdot ft)** **Please refer to the diagram in Figure 1 for spatial orientation and measurements.** #### Diagram Explanation: - The tetrahedron is situated in 3D space with the following dimensions: - Distance \( AB = 10 \) ft - Distance \( AC = 8 \) ft - Distance \( AD = 15 \) ft - The base lies along the \( xy \)-plane. - Axes: - \( x \)-axis aligns with \( A \to B \) - \( y \)-axis runs perpendicular from \( A \) in the \( xy \)-plane to \( C \) - \( z \)-axis is vertical, leading from \( A \) to \( D \) Use the provided axes and coordinates to determine the solution accurately. **Submit Answer Button:** After computing the required moment, insert the value into the input box and click ‘Submit’. **Provide Feedback Link:** Click here if you have any feedback regarding this problem. --- **Note:** When solving for moments in 3D problems, consider using vector cross product formulas and the position vectors of the points involved to ensure precision.
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