Linear mass density and dangling rope.

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SUMMARY

The discussion focuses on calculating the tension in a dangling rope of mass M and length L under the influence of gravity. The proposed equation, F(r) = (Mg/L)(r), accurately describes the tension at any position r on the rope, provided that r is measured upward from the bottom of the rope. This equation effectively illustrates the linear mass density of the rope and the distribution of gravitational force along its length.

PREREQUISITES
  • Understanding of linear mass density
  • Basic principles of mechanics, specifically tension and gravity
  • Knowledge of algebraic manipulation of equations
  • Familiarity with the concept of forces acting on objects
NEXT STEPS
  • Study the derivation of tension in strings and ropes under various conditions
  • Explore the concept of linear mass density in different materials
  • Learn about the effects of varying mass distributions on tension
  • Investigate real-world applications of tension in engineering and physics
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the mechanics of tension in ropes and strings.

Timothy S
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A rope of mass M and length of L is dangling from a branch. The only force acting on it is gravity. The question is how do you find the tension of the rope at any position on the rope.

My proposed equation is this: F(r) = (Mg/L)(r) where r is any position on the rope. Is this equation correct? If it is incorrect what equation would be able to describe what I am asking?
 
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Timothy S said:
A rope of mass M and length of L is dangling from a branch. The only force acting on it is gravity. The question is how do you find the tension of the rope at any position on the rope.

My proposed equation is this: F(r) = (Mg/L)(r) where r is any position on the rope. Is this equation correct? If it is incorrect what equation would be able to describe what I am asking?
It is correct if r is the distance measured upward from the bottom of the rope.

Chet
 

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