### Problem DescriptionA 560-N uniform rectangular sign that is 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 150-N rod as indicated in the diagram 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 there is a 2.00 m separation between the wall and the sign.### Diagram ExplanationThe diagram shows an "ICE CREAM SHOP" sign hanging vertically. The sign is supported by a horizontal rod which is attached to the wall. The rod is kept in position with the aid of a cable that makes a 30.0° angle with the vertical line from a point higher on the wall. The forces involved are:- The weight of the sign (560 N) acting downward at its center of gravity.- The weight of the rod (150 N) also acting downward at its center of gravity.- The tension (T) in the cable, which has components both vertically and horizontally. - The forces exerted by the hinge, which can be resolved into horizontal and vertical components.### Questions#### (a) Find the (magnitude of the) tension \( T \) in the cable.\[ T = \text{________} \, \text{N} \]#### (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:\[ \text{Horizontal component} = \text{________} \, \text{N} \]- Vertical component:\[ \text{Vertical component} = \text{________} \, \text{N} \]

Answered: Image /qna-images/answer/f823a1a9-7d71-42d8-995d-9f14c2aa0ac1.jpg

A 560-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 150-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.) 30.00 ICE CREAM SHOP (a) Find the (magnitude of the) tension T in 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

A 560-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 150-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.) 30.00 ICE CREAM SHOP (a) Find the (magnitude of the) tension T in 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

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.

Question

### Problem Description

A 560-N uniform rectangular sign that is 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 150-N rod as indicated in the diagram 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 there is a 2.00 m separation between the wall and the sign.

### Diagram Explanation

The diagram shows an "ICE CREAM SHOP" sign hanging vertically. The sign is supported by a horizontal rod which is attached to the wall. The rod is kept in position with the aid of a cable that makes a 30.0° angle with the vertical line from a point higher on the wall.

The forces involved are:
- The weight of the sign (560 N) acting downward at its center of gravity.
- The weight of the rod (150 N) also acting downward at its center of gravity.
- The tension (T) in the cable, which has components both vertically and horizontally.
- The forces exerted by the hinge, which can be resolved into horizontal and vertical components.

### Questions

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

\[ T = \text{________} \, \text{N} \]

#### (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:

\[ \text{Horizontal component} = \text{________} \, \text{N} \]

- Vertical component:

\[ \text{Vertical component} = \text{________} \, \text{N} \]

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