# Physics Problem: Suspended Sign with Cable Tension## Problem Statement:A 480-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.)![Diagram](https://i.imgur.com/VpR0Gdz.png)### Diagram Explanation- The image depicts a vertical wall with a rod extending horizontally to the right. The rod supports the sign labeled "ICE CREAM SHOP" hanging directly below it.- The cable, which supports the right end of the rod, forms a 30.0° angle with the vertical.- Annotations indicate the tension in the cable (T), the angle of 30.0°, and the uniform weights of the rod (110 N) and the sign (480 N).## Questions:### (a) Find the (magnitude of the) tension \( T \) in the cable.\[ T = \boxed{\ \ \ \ \ \ \ \ \ } \text{N} \]### (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.)- **Horizontal component**: \( \boxed{\ \ \ \ \ \ \ \ \ } \text{N} \)- **Vertical component**: \( \boxed{\ \ \ \ \ \ \ \ \ } \text{N} \)### Approach:1. **Free-Body Diagram**: Draw a free-body diagram for the system, showing all forces acting on the rod and sign.2. **Equilibrium Conditions**: Use the conditions of equilibrium (sum of forces and sum of moments/torques should be zero) to derive the necessary equations.3. **Solve for Tension**: Calculate the tension \( T \) in the cable.4. **Force Components**: Determine the horizontal and vertical force components at the

Given data as per question Weight of block = 480 N Weight of rod = 110 N Angle =300

A 480-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 480-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.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

# Physics Problem: Suspended Sign with Cable Tension

## Problem Statement:
A 480-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.)

![Diagram](https://i.imgur.com/VpR0Gdz.png)

### Diagram Explanation
- The image depicts a vertical wall with a rod extending horizontally to the right. The rod supports the sign labeled "ICE CREAM SHOP" hanging directly below it.
- The cable, which supports the right end of the rod, forms a 30.0° angle with the vertical.
- Annotations indicate the tension in the cable (T), the angle of 30.0°, and the uniform weights of the rod (110 N) and the sign (480 N).

## Questions:
### (a) Find the (magnitude of the) tension \( T \) in the cable.
\[ T = \boxed{\ \ \ \ \ \ \ \ \ } \text{N} \]

### (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.)
- **Horizontal component**: \( \boxed{\ \ \ \ \ \ \ \ \ } \text{N} \)
- **Vertical component**: \( \boxed{\ \ \ \ \ \ \ \ \ } \text{N} \)

### Approach:
1. **Free-Body Diagram**: Draw a free-body diagram for the system, showing all forces acting on the rod and sign.
2. **Equilibrium Conditions**: Use the conditions of equilibrium (sum of forces and sum of moments/torques should be zero) to derive the necessary equations.
3. **Solve for Tension**: Calculate the tension \( T \) in the cable.
4. **Force Components**: Determine the horizontal and vertical force components at the

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