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A 30.630.6 kg mass (?m) is suspended by the cable assembly as shown in the figure. The cables have no mass of their own. The cable to the left (?1T1) of the mass makes an angle of 0.00∘0.00∘ with the horizontal, and the cable to the right (?2T2)makes an angle (?2θ2) of 40.6∘40.6∘. If the mass is at rest, what is the tension in each of the cables, ?1T1 and ?2T2? The acceleration due to gravity is ?=9.81 m/s2g=9.81 m/s2.

A 30.630.6 kg mass (?m) is suspended by the cable assembly as shown in the figure. The cables have no mass of their own. The cable to the left (?1T1) of the mass makes an angle of 0.00∘0.00∘ with the horizontal, and the cable to the right (?2T2)makes an angle (?2θ2) of 40.6∘40.6∘. If the mass is at rest, what is the tension in each of the cables, ?1T1 and ?2T2? The acceleration due to gravity is ?=9.81 m/s2g=9.81 m/s2.

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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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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A 30.630.6 kg mass (?m) is suspended by the cable assembly as shown in the figure. The cables have no mass of their own. The cable to the left (?1T1) of the mass makes an angle of 0.00∘0.00∘ with the horizontal, and the cable to the right (?2T2)makes an angle (?2θ2) of 40.6∘40.6∘. If the mass is at rest, what is the tension in each of the cables, ?1T1 and ?2T2? The acceleration due to gravity is ?=9.81 m/s2g=9.81 m/s2.

### Diagram Description: Mechanics - Tension and Forces This diagram illustrates a physical setup used to demonstrate concepts of tension and forces in a physics context. 1. **Mass (m)**: - A pink-colored mass \( m \) is suspended and held in equilibrium by two tension forces. 2. **Tensions (\( T_1 \) and \( T_2 \))**: - \( T_1 \): Shown as an orange arrow, pointing horizontally to the left. This tension counteracts the horizontal component of the opposing tension \( T_2 \). - \( T_2 \): Represented by a pink arrow, pointing upwards and to the right at an angle \( \theta_2 \) to the horizontal. 3. **Angle (\( \theta_2 \))**: - The angle \( \theta_2 \) signifies the inclination of the string under tension \( T_2 \) with the horizontal direction. 4. **Supports**: - The entire setup is depicted between two vertical walls indicated in gray on either side, suggesting that the strings are attached to these supports. This configuration is typically used to explore the equilibrium of forces, tension in strings, and the components of forces acting at an angle. The angle and tensions can be manipulated to understand how forces balance in static conditions.
Transcribed Image Text:### Diagram Description: Mechanics - Tension and Forces This diagram illustrates a physical setup used to demonstrate concepts of tension and forces in a physics context. 1. **Mass (m)**: - A pink-colored mass \( m \) is suspended and held in equilibrium by two tension forces. 2. **Tensions (\( T_1 \) and \( T_2 \))**: - \( T_1 \): Shown as an orange arrow, pointing horizontally to the left. This tension counteracts the horizontal component of the opposing tension \( T_2 \). - \( T_2 \): Represented by a pink arrow, pointing upwards and to the right at an angle \( \theta_2 \) to the horizontal. 3. **Angle (\( \theta_2 \))**: - The angle \( \theta_2 \) signifies the inclination of the string under tension \( T_2 \) with the horizontal direction. 4. **Supports**: - The entire setup is depicted between two vertical walls indicated in gray on either side, suggesting that the strings are attached to these supports. This configuration is typically used to explore the equilibrium of forces, tension in strings, and the components of forces acting at an angle. The angle and tensions can be manipulated to understand how forces balance in static conditions.
### Tension Forces in a Rope The image presents two equations for tension forces, commonly used in physics and engineering problems to describe forces transmitted through a rope or cable: 1. **T₁ =** - This represents the tension force at one end of the rope or system. - The unit displayed is Newtons (N), indicating the force's magnitude. 2. **T₂ =** - This represents the tension force at the other end of the rope or system. - Similarly, the force's magnitude is measured in Newtons (N). These equations are typically used in problems involving equilibrium, where the sum of forces is zero, or in systems involving pulleys or dynamic loads. Understanding these tensions helps in solving and analyzing the mechanical behavior of structures.
Transcribed Image Text:### Tension Forces in a Rope The image presents two equations for tension forces, commonly used in physics and engineering problems to describe forces transmitted through a rope or cable: 1. **T₁ =** - This represents the tension force at one end of the rope or system. - The unit displayed is Newtons (N), indicating the force's magnitude. 2. **T₂ =** - This represents the tension force at the other end of the rope or system. - Similarly, the force's magnitude is measured in Newtons (N). These equations are typically used in problems involving equilibrium, where the sum of forces is zero, or in systems involving pulleys or dynamic loads. Understanding these tensions helps in solving and analyzing the mechanical behavior of structures.
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