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If we change the angle of the upper chain from 60 degrees to 45 degrees, determine the new expressions for the three tensions. (The images have background info used to help solve the practice problem. )

If we change the angle of the upper chain from 60 degrees to 45 degrees, determine the new expressions for the three tensions. (The images have background info used to help solve the practice problem. )

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
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If we change the angle of the upper chain from 60 degrees to 45 degrees, determine the new expressions for the three tensions. (The images have background info used to help solve the practice problem. )
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**Example 5.2: Two-Dimensional Equilibrium** In this example, we analyze the conditions for equilibrium where multiple forces act at a single point, specifically an engine suspended by chains. Figure 5.2 illustrates this scenario. **Explanation:** An engine is supported by three chains, each subjected to different tensions. We assume that the forces involved are two-dimensional and that the chains’ weights are negligible. **Figure 5.2:** (a) **Engine, Chains, and Ring:** The diagram shows an engine suspended by three chains. The chains form angles of 60° with the vertical and horizontal axes. (b) **Free-body Diagram for Chain:** This diagram represents the forces acting on the ring where the chains intersect. The forces are T₁, T₂, and T₃, which are the tensions in the respective chains. (c) **Free-body Diagram for Engine:** The diagram shows: - T₁ directed horizontally to the left. - T₂ acting vertically downward. - T₃ forming a 60° angle from the horizontal, represented by its components: - T₃ cos 60° along the x-axis. - T₃ sin 60° along the y-axis. **Given:** - Two wires are connected: a jack steel cable and a Pearl mountaineering rope. - Forces exerted: - T₁ = 30 N - T₂ = 39 N - T₃ = 10 N Explore the conditions that achieve equilibrium with respect to the forces at play, ensuring the net force acting on the system is zero. **Video Tutor Solution:** A QR code is provided to access a video solution explaining the example in detail.
Transcribed Image Text:**Example 5.2: Two-Dimensional Equilibrium** In this example, we analyze the conditions for equilibrium where multiple forces act at a single point, specifically an engine suspended by chains. Figure 5.2 illustrates this scenario. **Explanation:** An engine is supported by three chains, each subjected to different tensions. We assume that the forces involved are two-dimensional and that the chains’ weights are negligible. **Figure 5.2:** (a) **Engine, Chains, and Ring:** The diagram shows an engine suspended by three chains. The chains form angles of 60° with the vertical and horizontal axes. (b) **Free-body Diagram for Chain:** This diagram represents the forces acting on the ring where the chains intersect. The forces are T₁, T₂, and T₃, which are the tensions in the respective chains. (c) **Free-body Diagram for Engine:** The diagram shows: - T₁ directed horizontally to the left. - T₂ acting vertically downward. - T₃ forming a 60° angle from the horizontal, represented by its components: - T₃ cos 60° along the x-axis. - T₃ sin 60° along the y-axis. **Given:** - Two wires are connected: a jack steel cable and a Pearl mountaineering rope. - Forces exerted: - T₁ = 30 N - T₂ = 39 N - T₃ = 10 N Explore the conditions that achieve equilibrium with respect to the forces at play, ensuring the net force acting on the system is zero. **Video Tutor Solution:** A QR code is provided to access a video solution explaining the example in detail.
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