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Create a FBD for segment 1 that is attached to the lower end of the cord. Assume, for the moment, that the weight is in equilibrium.  Given:  Enumerate the segments as i=1,⋯,N from the lower to the upper end.   Let T0 be the tension at the lower end of the cord.   Let Ti be the tension at the upper end of segment i.   Let Fg,M be the weight of the mass on the end of the cord.

Create a FBD for segment 1 that is attached to the lower end of the cord. Assume, for the moment, that the weight is in equilibrium.  Given:  Enumerate the segments as i=1,⋯,N from the lower to the upper end.   Let T0 be the tension at the lower end of the cord.   Let Ti be the tension at the upper end of segment i.   Let Fg,M be the weight of the mass on the end of the cord.

College Physics
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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Create a FBD for segment 1 that is attached to the lower end of the cord. Assume, for the moment, that the weight is in equilibrium. 

Given: 

    • Enumerate the segments as i=1,⋯,N from the lower to the upper end.

 

    • Let T0 be the tension at the lower end of the cord.

 

    • Let Ti be the tension at the upper end of segment i.

 

    • Let Fg,M be the weight of the mass on the end of the cord.

 

  • Let Fg,i be the weight of segment i of the cord.
The image illustrates a rope supporting a weight, divided into several segments with tensions labeled \( T_0, T_1, T_2, T_3, \) and \( T_4 \). ### Components: 1. **Rope Segments**: The rope is divided into five segments, each segment carrying a weight of \( \frac{m}{N} \). 2. **Tensions**: - \( T_0 \): This is the tension at the bottom of the rope, directly above the mass \( M \). - \( T_1, T_2, T_3, T_4 \): These tensions increase progressively as they move up the rope, supporting the weight of the rope segments below them. 3. **Mass**: The mass \( M \) is attached to the bottom of the rope. 4. **Length**: The entire length of the rope is denoted by \( L \). ### Description: The diagram represents a physical system where a rope is hanging vertically and supporting a mass at its bottom. The rope's total weight is uniformly distributed across its length. Each segment sustains the weight of all parts below it, creating a gradient of tension from the top to the bottom. This type of system exemplifies concepts such as tension distribution in physics, where the tension in a rope or cable not only depends on the external load applied but also on the rope's own weight.
Transcribed Image Text:The image illustrates a rope supporting a weight, divided into several segments with tensions labeled \( T_0, T_1, T_2, T_3, \) and \( T_4 \). ### Components: 1. **Rope Segments**: The rope is divided into five segments, each segment carrying a weight of \( \frac{m}{N} \). 2. **Tensions**: - \( T_0 \): This is the tension at the bottom of the rope, directly above the mass \( M \). - \( T_1, T_2, T_3, T_4 \): These tensions increase progressively as they move up the rope, supporting the weight of the rope segments below them. 3. **Mass**: The mass \( M \) is attached to the bottom of the rope. 4. **Length**: The entire length of the rope is denoted by \( L \). ### Description: The diagram represents a physical system where a rope is hanging vertically and supporting a mass at its bottom. The rope's total weight is uniformly distributed across its length. Each segment sustains the weight of all parts below it, creating a gradient of tension from the top to the bottom. This type of system exemplifies concepts such as tension distribution in physics, where the tension in a rope or cable not only depends on the external load applied but also on the rope's own weight.
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