As shown, a member is fixed at the origin, point \( O \), and has an applied force \( \mathbf{F} \), the tension in the rope, applied at the free end, point \( B \).The force is given by \( \mathbf{F} = 130 \, \text{N} \, \mathbf{i} - 125 \, \text{N} \, \mathbf{j} + 70 \, \text{N} \, \mathbf{k} \). The dimensions are \( x_1 = 1.35 \, \text{m} \), \( y_1 = 1.70 \, \text{m} \), and \( z_1 = 1.15 \, \text{m} \).What is the moment about the origin due to the applied force \( \mathbf{F} \)?**Express the individual components of the Cartesian vector to three significant figures, separated by commas.**\[ \mathbf{M}_O = [ \, ] \, \text{N} \cdot \text{m} \] The image depicts a three-dimensional diagram commonly used in engineering mechanics to illustrate vector forces in a structure. Here is a detailed description of the diagram:- The diagram features a structure composed of several pipes connected with joints, forming an L-shape. - There are three main coordinate axes labeled as \( x \), \( y \), and \( z \), intersecting at the origin point \( O \). Each axis helps define the spatial orientation of the structure.- The structure connects at different points along the axes, with lengths indicated by \( x_1 \), \( y_1 \), and \( z_1 \). These lengths help determine the position and dimensions of the structure.- The point \( B \) is marked on the right end of the horizontal arm of the structure.- At point \( B \), a force vector \( \mathbf{F} \) is shown, indicating that an external force is applied in a specific direction.- The force vector illustrates both the magnitude and direction of the force acting on the structure.This setup is typically used in educational materials to analyze how external forces influence the equilibrium and stability of mechanical structures.

Force F = 130 N i - 125 N j + 70 N k x1=1.70 m , z1=1.15 m

As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 2) The force is given by F = 130 Ni - 125 Nj+70 N k. The dimensions are x₁ = 1.35 m, y₁ = 1.70 m, and 21 = 1.15 m. What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. ► View Available Hint(s) Mo =[ VE ΑΣΦ ↓↑ vec wwwwwwww.. ? i, j, k] N.m

As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 2) The force is given by F = 130 Ni - 125 Nj+70 N k. The dimensions are x₁ = 1.35 m, y₁ = 1.70 m, and 21 = 1.15 m. What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. ► View Available Hint(s) Mo =[ VE ΑΣΦ ↓↑ vec wwwwwwww.. ? i, j, k] N.m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

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As shown, a member is fixed at the origin, point \( O \), and has an applied force \( \mathbf{F} \), the tension in the rope, applied at the free end, point \( B \).

The force is given by \( \mathbf{F} = 130 \, \text{N} \, \mathbf{i} - 125 \, \text{N} \, \mathbf{j} + 70 \, \text{N} \, \mathbf{k} \). The dimensions are \( x_1 = 1.35 \, \text{m} \), \( y_1 = 1.70 \, \text{m} \), and \( z_1 = 1.15 \, \text{m} \).

What is the moment about the origin due to the applied force \( \mathbf{F} \)?

**Express the individual components of the Cartesian vector to three significant figures, separated by commas.**

\[ \mathbf{M}_O = [ \, ] \, \text{N} \cdot \text{m} \]

The image depicts a three-dimensional diagram commonly used in engineering mechanics to illustrate vector forces in a structure. Here is a detailed description of the diagram:

- The diagram features a structure composed of several pipes connected with joints, forming an L-shape.
- There are three main coordinate axes labeled as \( x \), \( y \), and \( z \), intersecting at the origin point \( O \). Each axis helps define the spatial orientation of the structure.
- The structure connects at different points along the axes, with lengths indicated by \( x_1 \), \( y_1 \), and \( z_1 \). These lengths help determine the position and dimensions of the structure.
- The point \( B \) is marked on the right end of the horizontal arm of the structure.
- At point \( B \), a force vector \( \mathbf{F} \) is shown, indicating that an external force is applied in a specific direction.
- The force vector illustrates both the magnitude and direction of the force acting on the structure.

This setup is typically used in educational materials to analyze how external forces influence the equilibrium and stability of mechanical structures.

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