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The figure below shows forces acting at various points on a metal bar. The angles α = 46°, β = 29°, γ = 17°. The length ℓ = 3.8 m. Find the net torque (in N · m) on the bar about the following axes.  (a) an axis through O perpendicular to the page (Find Magnitude and direction) (b) an axis through C perpendicular to the page (Find Magnitude and direction)

The figure below shows forces acting at various points on a metal bar. The angles α = 46°, β = 29°, γ = 17°. The length ℓ = 3.8 m. Find the net torque (in N · m) on the bar about the following axes.  (a) an axis through O perpendicular to the page (Find Magnitude and direction) (b) an axis through C perpendicular to the page (Find Magnitude and direction)

College Physics
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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The figure below shows forces acting at various points on a metal bar. The angles α = 46°, β = 29°, γ = 17°. The length ℓ = 3.8 m. Find the net torque (in N · m) on the bar about the following axes. 

(a) an axis through O perpendicular to the page (Find Magnitude and direction)
(b) an axis through C perpendicular to the page (Find Magnitude and direction)
### Diagram Explanation The diagram represents a horizontal rod with three forces acting on it. The forces are depicted as arrows, indicating both the magnitude and direction of each force. 1. **Force at Point O (30 N):** - This force is 30 Newtons, directed downwards and to the left, forming an angle \( \alpha \) with the horizontal axis. 2. **Force at Point C (25 N):** - This force is 25 Newtons, directed upwards and to the left, forming an angle \( \beta \) with the vertical axis. 3. **Force at the opposite end (10 N):** - This force is 10 Newtons, directed to the right, forming an angle \( \gamma \) with the horizontal axis. ### Rod and Points - The rod is depicted as a horizontal line with point \( O \) on the left end and \( C \) in the middle. - The total length of the rod is given as \( \ell \). - The distance from point \( O \) to point \( C \) is \( \ell/2 \). ### Forces and Geometry - The forces are positioned considering the symmetry and the points of action: - \( 30 \, \text{N} \) is applied at \( O \). - \( 25 \, \text{N} \) is applied at \( C \). - \( 10 \, \text{N} \) is applied at the right end. This diagram serves to illustrate the equilibrium condition or the effect of these forces on the rod, which may include calculations of torque, net force, or solving for unknown angles.
Transcribed Image Text:### Diagram Explanation The diagram represents a horizontal rod with three forces acting on it. The forces are depicted as arrows, indicating both the magnitude and direction of each force. 1. **Force at Point O (30 N):** - This force is 30 Newtons, directed downwards and to the left, forming an angle \( \alpha \) with the horizontal axis. 2. **Force at Point C (25 N):** - This force is 25 Newtons, directed upwards and to the left, forming an angle \( \beta \) with the vertical axis. 3. **Force at the opposite end (10 N):** - This force is 10 Newtons, directed to the right, forming an angle \( \gamma \) with the horizontal axis. ### Rod and Points - The rod is depicted as a horizontal line with point \( O \) on the left end and \( C \) in the middle. - The total length of the rod is given as \( \ell \). - The distance from point \( O \) to point \( C \) is \( \ell/2 \). ### Forces and Geometry - The forces are positioned considering the symmetry and the points of action: - \( 30 \, \text{N} \) is applied at \( O \). - \( 25 \, \text{N} \) is applied at \( C \). - \( 10 \, \text{N} \) is applied at the right end. This diagram serves to illustrate the equilibrium condition or the effect of these forces on the rod, which may include calculations of torque, net force, or solving for unknown angles.
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