### Problem DescriptionA 460-N uniform rectangular sign, measuring 4.00 m in width and 3.00 m in height, is suspended from a horizontal, 6.00-m-long, uniform, 140-N rod. The setup is depicted in the accompanying illustration. 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. The cable is attached to the very end of the 6.00-m-long rod, and there is a 2.00 m separation between the wall and the sign.### Diagram ExplanationThe diagram illustrates:- A vertical wall from which a horizontal rod extends.- The rod is 6.00 m in length, with a hinge at the wall and a cable attached to the opposite end.- An "ICE CREAM SHOP" sign hangs below the rod.- The cable forms a 30.0° angle with the vertical.- The system shows forces acting on the rod: tension in the cable ($ T $) and gravitational forces on the rod and sign.### Tasks**(a) Find the (magnitude of the) tension $ T $ in the cable.**- Solution box provided for input: $ \,\,\,\,\,$ N**(b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge.** - Positive directions: upward and rightward- Horizontal component: $ \,\,\,\,\,$ N- Vertical component: $ \,\,\,\,\,$ N### Additional Resources- Buttons for further guidance: "Need Help?", "Read It", "Master It"This problem involves understanding static equilibrium concepts and resolving forces into components to analyze the physical setup.

Answered: Image /qna-images/answer/ba65b2c7-a4c9-4fb8-b14c-96eb4e635bdc.jpg

A 460-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 140-N rod as indicated in the fiqure 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 wail from the sign.) 30.0 ICECREAM SHOP (a) Find the (magnitude of the) tension Tin the cable. (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 vertical component N. Need Help? Read It Master It

A 460-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 140-N rod as indicated in the fiqure 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 wail from the sign.) 30.0 ICECREAM SHOP (a) Find the (magnitude of the) tension Tin the cable. (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 vertical component N. Need Help? Read It Master It

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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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

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### Problem Description

A 460-N uniform rectangular sign, measuring 4.00 m in width and 3.00 m in height, is suspended from a horizontal, 6.00-m-long, uniform, 140-N rod. The setup is depicted in the accompanying illustration. 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. The cable is attached to the very end of the 6.00-m-long rod, and there is a 2.00 m separation between the wall and the sign.

### Diagram Explanation

The diagram illustrates:
- A vertical wall from which a horizontal rod extends.
- The rod is 6.00 m in length, with a hinge at the wall and a cable attached to the opposite end.
- An "ICE CREAM SHOP" sign hangs below the rod.
- The cable forms a 30.0° angle with the vertical.
- The system shows forces acting on the rod: tension in the cable ($ T $) and gravitational forces on the rod and sign.

### Tasks

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

- Solution box provided for input: $ \,\,\,\,\,$ N

**(b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge.**
- Positive directions: upward and rightward

- Horizontal component: $ \,\,\,\,\,$ N
- Vertical component: $ \,\,\,\,\,$ N

### Additional Resources

- Buttons for further guidance: "Need Help?", "Read It", "Master It"

This problem involves understanding static equilibrium concepts and resolving forces into components to analyze the physical setup.

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