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, 349.0°, and 55.6 for the x, y, and z axes, respectively. B. F D 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°, 849.0°, and y = 55.6°. Recall that a is the angle between the vector and the x axis, ẞ is the angle between the vector and the y axis, and 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 = i N, j N, k N 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, FA, acting along member DA, due to the applied force F = 9.60 i 13.5 j + 24.8 k N. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part. ANSWER: FDA =
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, 349.0°, and 55.6 for the x, y, and z axes, respectively. B. F D 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°, 849.0°, and y = 55.6°. Recall that a is the angle between the vector and the x axis, ẞ is the angle between the vector and the y axis, and 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 = i N, j N, k N 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, FA, acting along member DA, due to the applied force F = 9.60 i 13.5 j + 24.8 k N. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part. ANSWER: FDA =
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, 349.0°, and 55.6 for the x, y, and z axes,
respectively.
Transcribed Image Text:B.
F
D
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°, 849.0°, and y = 55.6°. Recall that
a is the angle between the vector and the x axis, ẞ is the angle between the vector and the y axis, and 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 =
i N, j N, k N
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, FA, acting along member DA, due to the applied force F = 9.60 i 13.5 j + 24.8 k N.
Express your answer to three significant figures and include the appropriate units.
You did not open hints for this part.
ANSWER:
FDA =
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