### Mechanics of a Uniform Boom Supported by a Cable**Problem Statement:**A 1,000-N uniform boom is angled at φ = 58.5° to the horizontal. It is supported by a cable at an angle θ = 31.5° to the horizontal. The boom is pivoted at the bottom, and it supports an object with a weight w = 1,950 N hanging from its top.**Diagram Explanation:**- The diagram shows the setup described in the problem, with the boom fixed at a pivot point on the bottom left.- The cable is attached from the top of the boom to an anchor point, creating the angle θ.- The angles φ and θ are marked for reference.- Lines indicate horizontal and vertical components of forces for aiding in calculation.**Tasks:**(a) Calculate the tension in the support cable.**Provided Answer:** - Initial Answer: 1.28012 kN- Feedback indicates this answer is incorrect and should be rechecked.(b) Determine the components of the reaction force exerted by the pivot on the boom. Assume the positive x-direction is to the right and the positive y-direction is upward. **Components Needed:**- Horizontal Component (kN)- Vertical Component (kN)**Solution Approach:**1. Use the principles of static equilibrium, noting that for a system in equilibrium, the sum of forces and the sum of moments (torques) must be zero.2. Break each force into its horizontal and vertical components.3. Analyze the forces along each direction and set up equations to solve for tension in the cable and reaction forces at the pivot.Ensure all calculations are precise and double-check each step to meet the problem's requirements.

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A 1,000-N uniform boom at p = 58.5° to the horizontal is supported by a cable at an angle e = 31.5° to the horizontal as shown in the figure below. The boom is pivoted at the bottom, and an object of weight w = 1,950 N hangs from its top. Pivot (a) Find the tension in the support cable. 1.28012 Your response differs from the correct answer by more than 10%. Double check your calculations. kN (b) Find the components of the reaction force exerted by the pivot on the boom. (Assume the positive x-direction is to the right and the positive y-direction is upward. Include the sign of the value in your answer.) horizontal component kN vertical component kN

A 1,000-N uniform boom at p = 58.5° to the horizontal is supported by a cable at an angle e = 31.5° to the horizontal as shown in the figure below. The boom is pivoted at the bottom, and an object of weight w = 1,950 N hangs from its top. Pivot (a) Find the tension in the support cable. 1.28012 Your response differs from the correct answer by more than 10%. Double check your calculations. kN (b) Find the components of the reaction force exerted by the pivot on the boom. (Assume the positive x-direction is to the right and the positive y-direction is upward. Include the sign of the value in your answer.) horizontal component kN vertical component kN

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter8: Rotational Equilibrium And Rotational Dynamics

Section: Chapter Questions

Problem 28P

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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

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### Mechanics of a Uniform Boom Supported by a Cable

**Problem Statement:**
A 1,000-N uniform boom is angled at φ = 58.5° to the horizontal. It is supported by a cable at an angle θ = 31.5° to the horizontal. The boom is pivoted at the bottom, and it supports an object with a weight w = 1,950 N hanging from its top.

**Diagram Explanation:**
- The diagram shows the setup described in the problem, with the boom fixed at a pivot point on the bottom left.
- The cable is attached from the top of the boom to an anchor point, creating the angle θ.
- The angles φ and θ are marked for reference.
- Lines indicate horizontal and vertical components of forces for aiding in calculation.

**Tasks:**
(a) Calculate the tension in the support cable.

**Provided Answer:**
- Initial Answer: 1.28012 kN
- Feedback indicates this answer is incorrect and should be rechecked.

(b) Determine the components of the reaction force exerted by the pivot on the boom. Assume the positive x-direction is to the right and the positive y-direction is upward.

**Components Needed:**
- Horizontal Component (kN)
- Vertical Component (kN)

**Solution Approach:**
1. Use the principles of static equilibrium, noting that for a system in equilibrium, the sum of forces and the sum of moments (torques) must be zero.
2. Break each force into its horizontal and vertical components.
3. Analyze the forces along each direction and set up equations to solve for tension in the cable and reaction forces at the pivot.

Ensure all calculations are precise and double-check each step to meet the problem's requirements.

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