The construction worker exerts a 20-lb force on the rope to hold the crate in equilibrium in the position shown. What is the weight of the crate? ### Mechanical Advantage in Adjustable PulleysThe image depicts a mechanical setup where a worker is maneuvering a large rectangular box using a rope and pulley system. The key elements of the illustration are described below for detailed analysis and educational purposes:#### Components:1. **Pulley System**: - The pulley is anchored above, allowing the rope to pass through it. - The setup is designed to lift or control the position of the large box.2. **Angles Involved**: - **15° Angle**: This angle is created by the rope on the pulley. - **30° Angle**: This is the angle at which the worker pulls the rope away from the box horizontally.3. **Worker Position**: - The worker, wearing safety gear including a helmet and work boots, stands a few feet away from the box, manipulating the rope to control the movement.#### Explanation of Diagram:The diagram helps explain the principle of mechanical advantage gained through the pulley system. By pulling at a specified angle, the worker can manipulate heavy loads with reduced effort. The angles also relate to tension and the distribution of force within the system:- **15° Angle**: Reduces the effective load the worker feels. This angle demonstrates how the pulley system redirects the force efficiently.- **30° Angle**: Shows the optimal pulling direction, influenced by ergonomic and mechanical considerations, to make lifting manageable while maintaining control of the load.This instructional illustration is beneficial in subjects like physics and engineering, demonstrating real-world applications of force, angles, and mechanical systems. Students can learn how manipulating angles and leverages in a pulley system simplifies difficult tasks, illustrating fundamental concepts of mechanical advantage and work-efficiency. This diagram represents a static equilibrium scenario involving forces. The system consists of three forces acting at a single point. Here's a detailed description:1. **Force T**: - This force is directed upwards and to the left. - It forms an angle of 5 degrees with the vertical (denoted by the dotted line).2. **Force W**: - This force is directed vertically downward. - It likely represents the weight (W) of an object.3. **Force of 20 lb**: - This force is directed downwards and to the right. - It forms an angle of 30 degrees with the horizontal (denoted by the dotted line).All vectors are presumed to be acting on a point in a two-dimensional plane. The angles provide the direction of each force in relation to either the vertical or horizontal axis, crucial for analyzing the system's equilibrium using principles of statics, such as the law of sines or cosines, or vector components. In this context, these angles and magnitudes can be used to find unknown forces or components by resolving them into x and y directions, then applying the equilibrium conditions (i.e., the sum of forces in any direction equals zero).

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The construction worker exerts a 20-lb force on the rope to hold the crate in equilibrium in the position shown. What is the weight of the crate?

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

The construction worker exerts a 20-lb force on the rope to hold the crate in equilibrium in the position shown. What is the weight of the crate?

### Mechanical Advantage in Adjustable Pulleys

The image depicts a mechanical setup where a worker is maneuvering a large rectangular box using a rope and pulley system. The key elements of the illustration are described below for detailed analysis and educational purposes:

#### Components:

1. **Pulley System**:
- The pulley is anchored above, allowing the rope to pass through it.
- The setup is designed to lift or control the position of the large box.

2. **Angles Involved**:
- **15° Angle**: This angle is created by the rope on the pulley.
- **30° Angle**: This is the angle at which the worker pulls the rope away from the box horizontally.

3. **Worker Position**:
- The worker, wearing safety gear including a helmet and work boots, stands a few feet away from the box, manipulating the rope to control the movement.

#### Explanation of Diagram:

The diagram helps explain the principle of mechanical advantage gained through the pulley system. By pulling at a specified angle, the worker can manipulate heavy loads with reduced effort. The angles also relate to tension and the distribution of force within the system:

- **15° Angle**: Reduces the effective load the worker feels. This angle demonstrates how the pulley system redirects the force efficiently.
- **30° Angle**: Shows the optimal pulling direction, influenced by ergonomic and mechanical considerations, to make lifting manageable while maintaining control of the load.

This instructional illustration is beneficial in subjects like physics and engineering, demonstrating real-world applications of force, angles, and mechanical systems. Students can learn how manipulating angles and leverages in a pulley system simplifies difficult tasks, illustrating fundamental concepts of mechanical advantage and work-efficiency.

This diagram represents a static equilibrium scenario involving forces.

The system consists of three forces acting at a single point. Here's a detailed description:

1. **Force T**:
- This force is directed upwards and to the left.
- It forms an angle of 5 degrees with the vertical (denoted by the dotted line).

2. **Force W**:
- This force is directed vertically downward.
- It likely represents the weight (W) of an object.

3. **Force of 20 lb**:
- This force is directed downwards and to the right.
- It forms an angle of 30 degrees with the horizontal (denoted by the dotted line).

All vectors are presumed to be acting on a point in a two-dimensional plane. The angles provide the direction of each force in relation to either the vertical or horizontal axis, crucial for analyzing the system's equilibrium using principles of statics, such as the law of sines or cosines, or vector components.

In this context, these angles and magnitudes can be used to find unknown forces or components by resolving them into x and y directions, then applying the equilibrium conditions (i.e., the sum of forces in any direction equals zero).

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