Calculating Tension Ratios for Equilibrium of Identical Bodies

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Homework Help Overview

The problem involves calculating the tension ratios in a system of identical bodies in equilibrium, specifically focusing on the tensions in ropes supporting these bodies. The subject area includes mechanics and equilibrium conditions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the tensions T1 and T2, with some attempting to determine the correct value of T2 based on the weights involved. Questions arise about whether to include the weight of the bodies in the tension calculations and how the configuration of the system affects these tensions.

Discussion Status

The discussion is ongoing, with various interpretations of the tension values being explored. Some participants suggest that T2 must support the total weight, while others propose different ratios based on their assumptions. There is no explicit consensus on the correct ratio, as conflicting answers have been presented.

Contextual Notes

Participants note the importance of specific angles and configurations in determining the tensions, indicating that certain assumptions may be necessary for a complete analysis. The presence of a rigid support and the arrangement of the bodies are also mentioned as factors that influence the calculations.

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Homework Statement



Identical K,L and M bodies with a weight of P are in equilibrium . If the tension in the rope S1 is T1 and S2 is T2, then what is the ratio T1/T2? (The picture is below)

Homework Equations


The Attempt at a Solution



T1 equals P. But I am stuck with T2. I cannot decide whether it is 2P or 3P. Do we have to add the weight of K to T2? If we add, it will be 3P.
 

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S2 is the uppermost vertical string and so must support all of the weight. Its tension will be 3P.
 
Then the answer is 1/3.But according to my book the answer is 1/2.
 
the pulley is attached to a rigid support.T2 has a weight of 2P
 
Let us call A the node above K and B the node above L. Let us assume that the angle between a horizontal line and the rope connecting A to B is 45 degrees (without this value you cannot compute a solution). Then you only have to write the equilibrium conditions at nodes A (first) and B (second).
The ratio is 1/2.
 
Many Thanks
 

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