Finding minimum values for problems

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SUMMARY

The discussion focuses on calculating the minimum length of a chain sling required to lift a 1000N weight without exceeding a tension of 1300N. Participants suggest using the formula T sin(theta) = W/2 to derive the angle at which the sling meets the block, which is crucial for determining the sling's length. The conversation emphasizes that calculus is unnecessary for this problem, as the maximum tension provides sufficient information to solve for the angle and subsequently the length of the chain sling.

PREREQUISITES
  • Understanding of basic physics concepts related to tension and weight.
  • Familiarity with trigonometric functions, specifically sine.
  • Knowledge of how to manipulate equations to isolate variables.
  • Basic geometry skills, particularly involving triangles.
NEXT STEPS
  • Study the derivation of tension formulas in static equilibrium scenarios.
  • Learn about trigonometric relationships in right triangles.
  • Explore practical applications of chain slings in lifting operations.
  • Investigate the implications of angle adjustments on tension and length in lifting systems.
USEFUL FOR

This discussion is beneficial for engineering students, physics enthusiasts, and professionals involved in lifting operations or rigging, particularly those seeking to optimize sling configurations for safety and efficiency.

tooperoo
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Homework Statement


Hi guys, really stuck on this one.

A 1000N black is to be lifted using a chain sling (as shown). If the tension in the chain sling is not to exceed 1300N, find the shortest sling ABC that can be used.
A is the most left point, B is the most right point and C is the top point.




Homework Equations





The Attempt at a Solution



I think i have to take the derivative of something to find the minimum but have no idea how to go about that.

Picture_2.jpg

 
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You shouldn't need to use calculus on this one. Since you've been given the maximal value of the tension, start by writing an expression that gives the tension in the sling as a function of the angle where the sling meets the block. What is the value of the angle that corresponds to the given maximal tension?
 
I think I've got it.

With this formula
T sin(theta) = W/2
i can get the angle cause i know the max tension, but then how do i get the length of the chain from that?
 
tooperoo said:
I think I've got it.

With this formula
T sin(theta) = W/2
i can get the angle cause i know the max tension, but then how do i get the length of the chain from that?
If you know the angle and at least one triangle side length...
 

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