**Educational Exercise: Analysis of Forces on a Suspended Sign****Scenario Overview:**A 460-N uniform rectangular sign, measuring 4.00 meters in width and 3.00 meters in height, is suspended from a horizontal rod. This rod is 6.00 meters long, uniform, and has a weight of 120 N. The suspension system includes a hinge on the left end of the rod, and the right end is supported by a thin cable. The cable forms a 30.0° angle with the vertical. It is assumed that the cable is attached to the rod's very end, and there is a 2.00-meter gap between the wall and the sign.**Diagram Explanation:**The diagram shows a side view of the sign and suspension system:- The "ICE CREAM SHOP" sign hangs vertically beneath the rod.- A thin cable supports the right end of the rod, labeled with tension "T."- The cable forms a 30.0° angle with a vertical line (indicating the angle of elevation).- The hinge on the left end connects the rod to the wall.**Problem Tasks:**(a) Calculate the tension "T" in the cable.- Find the magnitude of the tension. **Answer Box:** Tension: [_______] N(b) Determine the horizontal and vertical components of the force exerted on the left end of the rod by the hinge.- Define positive directions as upward and to the right. **Answer Boxes:** Horizontal Component: [_______] N Vertical Component: [_______] NThis task involves understanding static equilibrium, vector decomposition, and force analysis to solve for unknown quantities.

Given: Force on the uniform rectangular sign = 460 N Width = 4 m Height of sign = 3 m Length of the…

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, 120-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 T ICE CREAM SHOP (a) Find the tension T in the cable. (Give the magnitude of the tension.) (b) Find the horizontal and vertical components of 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

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, 120-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 T ICE CREAM SHOP (a) Find the tension T in the cable. (Give the magnitude of the tension.) (b) Find the horizontal and vertical components of 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

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

**Educational Exercise: Analysis of Forces on a Suspended Sign**

**Scenario Overview:**

A 460-N uniform rectangular sign, measuring 4.00 meters in width and 3.00 meters in height, is suspended from a horizontal rod. This rod is 6.00 meters long, uniform, and has a weight of 120 N. The suspension system includes a hinge on the left end of the rod, and the right end is supported by a thin cable. The cable forms a 30.0° angle with the vertical. It is assumed that the cable is attached to the rod's very end, and there is a 2.00-meter gap between the wall and the sign.

**Diagram Explanation:**

The diagram shows a side view of the sign and suspension system:

- The "ICE CREAM SHOP" sign hangs vertically beneath the rod.
- A thin cable supports the right end of the rod, labeled with tension "T."
- The cable forms a 30.0° angle with a vertical line (indicating the angle of elevation).
- The hinge on the left end connects the rod to the wall.

**Problem Tasks:**

(a) Calculate the tension "T" in the cable.
- Find the magnitude of the tension.

**Answer Box:**
Tension: [_______] N

(b) Determine the horizontal and vertical components of the force exerted on the left end of the rod by the hinge.
- Define positive directions as upward and to the right.

**Answer Boxes:**
Horizontal Component: [_______] N
Vertical Component: [_______] N

This task involves understanding static equilibrium, vector decomposition, and force analysis to solve for unknown quantities.

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