### Problem Statement**Drawbridge Mechanics**A 550 kg drawbridge has a hinge at one end and a cable attached to the other. It is stuck in a position where it makes an angle of 30° with the vertical. The cable pulling on the far end of the bridge is horizontal. Find the tension in the cable as well as the vertical and horizontal components of force from the hinge.**Hints:**1. Be careful with your sinθ terms in this problem. Drawing a good picture should help.2. The length of the bridge will cancel out. Just use L.### Solution ExplanationTo solve this problem, follow these steps:1. **Draw a Diagram:** - Represent the drawbridge as a rectangular bar with a hinge on one end and a cable attached to the other. - The drawbridge forms a 30° angle with the vertical direction. - Label the forces acting on the drawbridge: the weight (550 kg * 9.81 m/s² = 5395.5 N) acting downward at the center of mass (which is at the midpoint of the bridge), the tension (T) in the cable pulling horizontally, and the reaction forces at the hinge (Hₓ and Hᵧ).2. **Resolve Forces:** - Resolve the weight (W) acting at the midpoint of the drawbridge. - The vertical component of the hinge force will balance the weight of the drawbridge. - The horizontal component of the hinge force and the tension in the cable will balance each other out.3. **Equilibrium Equations:** - Sum of vertical forces = 0: Hᵧ - W = 0 - Therefore, Hᵧ = W = 5395.5 N - Sum of horizontal forces = 0: Hₓ - T = 0 - Therefore, Hₓ = T4. **Torque Equilibrium:** - Taking moments about the hinge to eliminate the hinge force components: - Consider the torque due to the weight W acting at a distance of L/2 from the hinge. - Consider the torque due to the tension T acting at a distance of L from the hinge. - Sum of torques = 0: (W * L/2) * sin(30°) - T * L = 0 - Solving gives: (539

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3. A 550 kg drawbridge has a hinge at one end and a cable attached to the other. It is stuck in a position where it makes an angle of 30° with the vertical. The cable pulling on the far end of the bridge is horizontal. Find the tension in the cable as well as the vertical and horizontal components of force from the hinge.

3. A 550 kg drawbridge has a hinge at one end and a cable attached to the other. It is stuck in a position where it makes an angle of 30° with the vertical. The cable pulling on the far end of the bridge is horizontal. Find the tension in the cable as well as the vertical and horizontal components of force from the hinge.

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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Concept explainers

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

### Problem Statement

**Drawbridge Mechanics**

A 550 kg drawbridge has a hinge at one end and a cable attached to the other. It is stuck in a position where it makes an angle of 30° with the vertical. The cable pulling on the far end of the bridge is horizontal. Find the tension in the cable as well as the vertical and horizontal components of force from the hinge.

**Hints:**
1. Be careful with your sinθ terms in this problem. Drawing a good picture should help.
2. The length of the bridge will cancel out. Just use L.

### Solution Explanation

To solve this problem, follow these steps:

1. **Draw a Diagram:**
- Represent the drawbridge as a rectangular bar with a hinge on one end and a cable attached to the other.
- The drawbridge forms a 30° angle with the vertical direction.
- Label the forces acting on the drawbridge: the weight (550 kg * 9.81 m/s² = 5395.5 N) acting downward at the center of mass (which is at the midpoint of the bridge), the tension (T) in the cable pulling horizontally, and the reaction forces at the hinge (Hₓ and Hᵧ).

2. **Resolve Forces:**
- Resolve the weight (W) acting at the midpoint of the drawbridge.
- The vertical component of the hinge force will balance the weight of the drawbridge.
- The horizontal component of the hinge force and the tension in the cable will balance each other out.

3. **Equilibrium Equations:**
- Sum of vertical forces = 0: Hᵧ - W = 0
- Therefore, Hᵧ = W = 5395.5 N
- Sum of horizontal forces = 0: Hₓ - T = 0
- Therefore, Hₓ = T

4. **Torque Equilibrium:**
- Taking moments about the hinge to eliminate the hinge force components:
- Consider the torque due to the weight W acting at a distance of L/2 from the hinge.
- Consider the torque due to the tension T acting at a distance of L from the hinge.
- Sum of torques = 0: (W * L/2) * sin(30°) - T * L = 0
- Solving gives: (539

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