A 580-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 110-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) (a) Find the (magnitude of the) tension T in the cable. N(b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.) ### Understanding Tension in a Hanging SignIn this diagram, we are analyzing the tension in the supporting wire of a hanging sign. The image shows a sign labeled "ICE CREAM SHOP" suspended by a wire attached to a wall. The wire forms an angle of 30.0° with the wall.#### Diagram Breakdown:- **Building Wall**: Represented by a vertical red structure on the left side of the image.- **Angle**: The wire makes an angle of 30.0° with the wall.- **Tension (T)**: Represented by the variable T, is the force exerted along the wire.- **Sign**: The rectangular sign hanging perpendicular to the wire, labeled "ICE CREAM SHOP".### Concepts Involved:1. **Tension in Physics**: - Tension is the force conducted along the wire. It acts to support the weight of the sign.2. **Analyzing Forces**: - The forces acting on the system include the weight of the sign (acting vertically downward) and the tension in the wire. - The tension can be resolved into two components: - Horizontal Component (T_cos(30°)) - Vertical Component (T_sin(30°))3. **Static Equilibrium**: - For the sign to be in static equilibrium, the sum of forces in both the horizontal and vertical directions must be zero. - This means that the vertical component of the tension must balance the weight of the sign, and the horizontal component must be balanced by the reaction force at the point of attachment on the wall.This diagram can be used in educational settings to explain concepts such as tension, vector decomposition, and static equilibrium in physics.

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Answered: A 580-N uniform rectangular sign 4.00 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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A 580-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 110-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.)

(a) Find the (magnitude of the) tension T in the cable.
N

(b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.)

### Understanding Tension in a Hanging Sign

In this diagram, we are analyzing the tension in the supporting wire of a hanging sign. The image shows a sign labeled "ICE CREAM SHOP" suspended by a wire attached to a wall. The wire forms an angle of 30.0° with the wall.

#### Diagram Breakdown:
- **Building Wall**: Represented by a vertical red structure on the left side of the image.
- **Angle**: The wire makes an angle of 30.0° with the wall.
- **Tension (T)**: Represented by the variable T, is the force exerted along the wire.
- **Sign**: The rectangular sign hanging perpendicular to the wire, labeled "ICE CREAM SHOP".

### Concepts Involved:
1. **Tension in Physics**:
- Tension is the force conducted along the wire. It acts to support the weight of the sign.
2. **Analyzing Forces**:
- The forces acting on the system include the weight of the sign (acting vertically downward) and the tension in the wire.
- The tension can be resolved into two components:
- Horizontal Component (T_cos(30°))
- Vertical Component (T_sin(30°))
3. **Static Equilibrium**:
- For the sign to be in static equilibrium, the sum of forces in both the horizontal and vertical directions must be zero.
- This means that the vertical component of the tension must balance the weight of the sign, and the horizontal component must be balanced by the reaction force at the point of attachment on the wall.

This diagram can be used in educational settings to explain concepts such as tension, vector decomposition, and static equilibrium in physics.

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