Dot Product Learning Goal: To use the dot product to find the components of forces acting in arbitrary directions. A three-legged structure is shown below. It is attached to the ground at points B = (4.04, 0, 0) and C = (-4.04, 0, 0) and connected to the ceiling at point A-(4.92, 3.79, 4.87). The three legs connect at point D=(0, 3.23, 2.00), where two forces, F and P, act. Force F is given by F 9.60 i 13.5j+24.8 k N; P has magnitude 50.0 N and direction angles a=120.0°, 3-49.0°, and y=55.6° for the x, y, and z axes, respectively. Mastering Assignment #1 D Page 4 of 9 A Part A - Finding the Cartesian components of a force described by direction angles Find the Cartesian components of force P acting in the x, y, and z directions given P-50.0 N. a 120.0°, 349.0°. and y-55.6. Recall that a is the angle between the vector and the x axis, 3 is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. Express your answers, separated by commas, to three significant figures. You did not open hints for this part. ANSWER: P iN,j N, KN Part B - Finding the angle between forces Find the angle between forces F and P. Express your answer to three significant figures in degrees. You did not open hints for this part. ANSWER: 0- Part C - Determining the force along a member Determine the magnitude, FDA, acting along member DA, due to the applied force F-9.60 i-13.5j+24.8 kN. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part. ANSWER: FDA- Part D - Finding the component of a force perpendicular to a direction Given F-9.60 i -13.5j+24.8 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-F₁+F) with respect to DA equals F. Express your answer in component form.
Dot Product Learning Goal: To use the dot product to find the components of forces acting in arbitrary directions. A three-legged structure is shown below. It is attached to the ground at points B = (4.04, 0, 0) and C = (-4.04, 0, 0) and connected to the ceiling at point A-(4.92, 3.79, 4.87). The three legs connect at point D=(0, 3.23, 2.00), where two forces, F and P, act. Force F is given by F 9.60 i 13.5j+24.8 k N; P has magnitude 50.0 N and direction angles a=120.0°, 3-49.0°, and y=55.6° for the x, y, and z axes, respectively. Mastering Assignment #1 D Page 4 of 9 A Part A - Finding the Cartesian components of a force described by direction angles Find the Cartesian components of force P acting in the x, y, and z directions given P-50.0 N. a 120.0°, 349.0°. and y-55.6. Recall that a is the angle between the vector and the x axis, 3 is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. Express your answers, separated by commas, to three significant figures. You did not open hints for this part. ANSWER: P iN,j N, KN Part B - Finding the angle between forces Find the angle between forces F and P. Express your answer to three significant figures in degrees. You did not open hints for this part. ANSWER: 0- Part C - Determining the force along a member Determine the magnitude, FDA, acting along member DA, due to the applied force F-9.60 i-13.5j+24.8 kN. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part. ANSWER: FDA- Part D - Finding the component of a force perpendicular to a direction Given F-9.60 i -13.5j+24.8 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-F₁+F) with respect to DA equals F. Express your answer in component form.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Dot Product
Learning Goal:
To use the dot product to find the components of forces acting in arbitrary directions.
A three-legged structure is shown below. It is attached to the ground at points B = (4.04, 0, 0) and C = (-4.04, 0, 0) and connected to the ceiling at point
A-(4.92, 3.79, 4.87). The three legs connect at point D=(0, 3.23, 2.00), where two forces, F and P, act. Force F is given by
F 9.60 i 13.5j+24.8 k N; P has magnitude 50.0 N and direction angles a=120.0°, 3-49.0°, and y=55.6° for the x, y, and z axes,
respectively.
Mastering Assignment #1
D
Page 4 of 9
A
Part A - Finding the Cartesian components of a force described by direction angles
Find the Cartesian components of force P acting in the x, y, and z directions given P-50.0 N. a 120.0°, 349.0°. and y-55.6. Recall that
a is the angle between the vector and the x axis, 3 is the angle between the vector and the y axis, and y is the angle between the vector and the z axis.
Express your answers, separated by commas, to three significant figures.
You did not open hints for this part.
ANSWER:
P
iN,j N, KN
Part B - Finding the angle between forces
Find the angle between forces F and P.
Express your answer to three significant figures in degrees.
You did not open hints for this part.
ANSWER:
0-
Part C - Determining the force along a member
Determine the magnitude, FDA, acting along member DA, due to the applied force F-9.60 i-13.5j+24.8 kN.
Express your answer to three significant figures and include the appropriate units.
You did not open hints for this part.
ANSWER:
FDA-
Part D - Finding the component of a force perpendicular to a direction
Given F-9.60 i -13.5j+24.8 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-F₁+F) with respect to DA equals F. Express your answer in component form.
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