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Learning Goal: Part A - Finding the Cartesian components of a force described by direction angles To use the dot product to find the components of forces acting in arbitrary directions. Find the Cartesian components of force P acting in the x, y, and z directions given P = 35.0 N, a = 128.0°, B= 41.0°, and y= 76.9°. Recall that a is the angle between the vector and the x axis, B is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. A three-legged structure is shown below. It is attached to the ground at points B = (4.05 , 0, 0) and C = (-4.05 , 0, 0) and connected to the ceiling at point A = (-4.67 , 4.21 , 5.85). The three legs connect at point D = (0, 3.60, 3.50), where two forces, F and P, act. Force F is given by F = 3.40 i – 14.5 j+24.0 k N; P has magnitude 35.0N and direction angles a = 128.0°, B= 41.0°, and y= 76.9° for the x, y, and z axes, respectively.(Figure 1) Express your answers, separated by commas, to three significant figures. • View Available Hint(s) vec P = i N, jN, k N Figure < 1 of 1 > Submit Part B - Finding the angle between forces Find the angle 0 between forces F and P. Express your answer to three significant figures in degrees. • View Available Hint(s) D. vec B. Submit 圓

Learning Goal: Part A - Finding the Cartesian components of a force described by direction angles To use the dot product to find the components of forces acting in arbitrary directions. Find the Cartesian components of force P acting in the x, y, and z directions given P = 35.0 N, a = 128.0°, B= 41.0°, and y= 76.9°. Recall that a is the angle between the vector and the x axis, B is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. A three-legged structure is shown below. It is attached to the ground at points B = (4.05 , 0, 0) and C = (-4.05 , 0, 0) and connected to the ceiling at point A = (-4.67 , 4.21 , 5.85). The three legs connect at point D = (0, 3.60, 3.50), where two forces, F and P, act. Force F is given by F = 3.40 i – 14.5 j+24.0 k N; P has magnitude 35.0N and direction angles a = 128.0°, B= 41.0°, and y= 76.9° for the x, y, and z axes, respectively.(Figure 1) Express your answers, separated by commas, to three significant figures. • View Available Hint(s) vec P = i N, jN, k N Figure < 1 of 1 > Submit Part B - Finding the angle between forces Find the angle 0 between forces F and P. Express your answer to three significant figures in degrees. • View Available Hint(s) D. vec B. Submit 圓

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter8: Centroids And Distributed Loads
Section: Chapter Questions
Problem 8.73P
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I Review Learning Goal: Part A - Finding the Cartesian components of a force described by direction angles To use the dot product to find the components of forces acting in arbitrary directions. 35.0 N, α- Find the Cartesian components of force P acting in the x, y, and z directions given P B = 41.0°, and y= 76.9°. Recall that a is the angle between the vector and the x axis, B is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. 128.0°, A three-legged structure is shown below. It is attached to the ground at points B = (4.05 , 0, 0) and C = (-4.05 , 0, 0) and connected to the ceiling at point A = (-4.67 , 4.21 , 5.85). The three legs connect at point D = (0, 3.60, 3.50), where two forces, F and P, act. Force F is given by F = 3.40 i – 14.5 j+ 24.0 k N; P has magnitude 35.0 N and direction angles a = 128.0°, ß= 41.0°, and y= 76.9° for the x, y, and z axes, respectively.(Figure 1) Express your answers, separated by commas, to three significant figures. • View Available Hint(s) |ν ΑΣΦ ? vec P = iN, j N, k N Figure 1 of 1 Submit Part B - Finding the angle between forces Find the angle 0 between forces F and P. Express your answer to three significant figures in degrees. F • View Available Hint(s) D Vo AEO ? vec B 0 = Submit
Transcribed Image Text:I Review Learning Goal: Part A - Finding the Cartesian components of a force described by direction angles To use the dot product to find the components of forces acting in arbitrary directions. 35.0 N, α- Find the Cartesian components of force P acting in the x, y, and z directions given P B = 41.0°, and y= 76.9°. Recall that a is the angle between the vector and the x axis, B is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. 128.0°, A three-legged structure is shown below. It is attached to the ground at points B = (4.05 , 0, 0) and C = (-4.05 , 0, 0) and connected to the ceiling at point A = (-4.67 , 4.21 , 5.85). The three legs connect at point D = (0, 3.60, 3.50), where two forces, F and P, act. Force F is given by F = 3.40 i – 14.5 j+ 24.0 k N; P has magnitude 35.0 N and direction angles a = 128.0°, ß= 41.0°, and y= 76.9° for the x, y, and z axes, respectively.(Figure 1) Express your answers, separated by commas, to three significant figures. • View Available Hint(s) |ν ΑΣΦ ? vec P = iN, j N, k N Figure 1 of 1 Submit Part B - Finding the angle between forces Find the angle 0 between forces F and P. Express your answer to three significant figures in degrees. F • View Available Hint(s) D Vo AEO ? vec B 0 = Submit
Review Learning Goal: Part C - Determining the force along a member To use the dot product to find the components of forces acting in arbitrary directions. Determine the magnitude, FDA, acting along member DA, due to the applied force F = 3.40 i – 14.5 j+ 24.0 k N. A three-legged structure is shown below. It is attached to the ground at points B = (4.05 , 0, 0) and C = (-4.05 , 0, 0) and connected to the ceiling at point A = (-4.67 , 4.21 , 5.85). The three legs connect at point D = (0, 3.60, 3.50), where two forces, F and P, act. Force F is given by F = 3.40 i – 14.5 j+ 24.0 k N; P has magnitude 35.0 N and direction angles a = 128.0°, B = 41.0°, and y = 76.9° for the x, y, and z axes, respectively.(Figure 1) Express your answer to three significant figures and include the appropriate units. %3D • View Available Hint(s) μΑ FDA Value Units Submit Figure 1 of 1 Part D - Finding the component of a force perpendicular to a direction A Given F = 3.40 i – 14.5 j + 24.0 kN, find the component of F that acts perpendicular to member DA such that the vector addition of the perpendicular and parallel components of F (F = F +F) with respect to DA equals F. Express your answer in component form. Express your answers, separated by commas, to three significant figures. F • View Available Hint(s) vec ? B FIDA i N, j N, k N Submit
Transcribed Image Text:Review Learning Goal: Part C - Determining the force along a member To use the dot product to find the components of forces acting in arbitrary directions. Determine the magnitude, FDA, acting along member DA, due to the applied force F = 3.40 i – 14.5 j+ 24.0 k N. A three-legged structure is shown below. It is attached to the ground at points B = (4.05 , 0, 0) and C = (-4.05 , 0, 0) and connected to the ceiling at point A = (-4.67 , 4.21 , 5.85). The three legs connect at point D = (0, 3.60, 3.50), where two forces, F and P, act. Force F is given by F = 3.40 i – 14.5 j+ 24.0 k N; P has magnitude 35.0 N and direction angles a = 128.0°, B = 41.0°, and y = 76.9° for the x, y, and z axes, respectively.(Figure 1) Express your answer to three significant figures and include the appropriate units. %3D • View Available Hint(s) μΑ FDA Value Units Submit Figure 1 of 1 Part D - Finding the component of a force perpendicular to a direction A Given F = 3.40 i – 14.5 j + 24.0 kN, find the component of F that acts perpendicular to member DA such that the vector addition of the perpendicular and parallel components of F (F = F +F) with respect to DA equals F. Express your answer in component form. Express your answers, separated by commas, to three significant figures. F • View Available Hint(s) vec ? B FIDA i N, j N, k N Submit
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