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4. Assuming the crate weighs 100 lbs, calculate the tension in each example and explain if a directional advantage exists or not. TEND (b) (e) (d) Figure 4. Pulleys (e)

4. Assuming the crate weighs 100 lbs, calculate the tension in each example and explain if a directional advantage exists or not. TEND (b) (e) (d) Figure 4. Pulleys (e)

Structural Analysis
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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**Exercise: Pulleys and Tension Calculation** 1. **Problem Statement:** Assuming the crate weighs 100 lbs, calculate the tension in each example and explain if a directional advantage exists or not. 2. **Diagram Description:** - **Figure 4: Pulleys** - **Diagram (a):** A simple single fixed pulley system. The rope is attached to the crate at one end and is looped over a pulley. The tension \( T \) is shown pulling upwards on the crate. - **Diagram (b):** A single movable pulley system with the crate directly attached to the pulley. The rope forms a loop around the pulley. The tension \( T \) pulls upwards with the force applied downwards on the opposite end. - **Diagram (c):** A combined pulley system with one fixed and one movable pulley. The rope is looped through both pulleys and attached to the ceiling at the other end. The tension \( T \) acts upwards on the crate with the applied force. - **Diagram (d):** Similar to (c), but with two movable pulleys and one fixed pulley. The tension \( T \) remains consistent with the upward pull. - **Diagram (e):** A complex system with multiple fixed and movable pulleys, enhancing the mechanical advantage with tension \( T \) acting upwards on the crate. 3. **Analysis:** - **Calculating Tension:** Each pulley setup has a different mechanical advantage that affects the tension in the rope. For instance, simple pulleys may not change the force needed but can change its direction. Complex systems with multiple pulleys can reduce the force necessary to lift the crate by distributing the weight across more ropes. - **Directional Advantage:** This term refers to whether the force applied (usually downward) creates a corresponding upward movement of the load. Fixed pulleys provide directional advantages by allowing a person to pull down to lift the load up, while movable pulleys reduce the force needed to lift the load without changing the direction of the force. By examining these pulley systems, one can determine how different configurations affect the efficiency of lifting a load.
Transcribed Image Text:**Exercise: Pulleys and Tension Calculation** 1. **Problem Statement:** Assuming the crate weighs 100 lbs, calculate the tension in each example and explain if a directional advantage exists or not. 2. **Diagram Description:** - **Figure 4: Pulleys** - **Diagram (a):** A simple single fixed pulley system. The rope is attached to the crate at one end and is looped over a pulley. The tension \( T \) is shown pulling upwards on the crate. - **Diagram (b):** A single movable pulley system with the crate directly attached to the pulley. The rope forms a loop around the pulley. The tension \( T \) pulls upwards with the force applied downwards on the opposite end. - **Diagram (c):** A combined pulley system with one fixed and one movable pulley. The rope is looped through both pulleys and attached to the ceiling at the other end. The tension \( T \) acts upwards on the crate with the applied force. - **Diagram (d):** Similar to (c), but with two movable pulleys and one fixed pulley. The tension \( T \) remains consistent with the upward pull. - **Diagram (e):** A complex system with multiple fixed and movable pulleys, enhancing the mechanical advantage with tension \( T \) acting upwards on the crate. 3. **Analysis:** - **Calculating Tension:** Each pulley setup has a different mechanical advantage that affects the tension in the rope. For instance, simple pulleys may not change the force needed but can change its direction. Complex systems with multiple pulleys can reduce the force necessary to lift the crate by distributing the weight across more ropes. - **Directional Advantage:** This term refers to whether the force applied (usually downward) creates a corresponding upward movement of the load. Fixed pulleys provide directional advantages by allowing a person to pull down to lift the load up, while movable pulleys reduce the force needed to lift the load without changing the direction of the force. By examining these pulley systems, one can determine how different configurations affect the efficiency of lifting a load.
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