Finding minimum values for problems

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Homework Help Overview

The problem involves determining the shortest length of a chain sling required to lift a 1000N weight, given that the tension in the sling must not exceed 1300N. The setup includes points A, B, and C, representing different positions of the sling.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need for calculus to find minimum values but question whether it is necessary. There is mention of deriving a tension expression based on the angle of the sling and its relationship to the weight being lifted.

Discussion Status

Some participants have offered guidance on formulating the problem by suggesting the use of trigonometric relationships to express tension in terms of the angle. There is ongoing exploration of how to derive the length of the chain from the angle once it is determined.

Contextual Notes

Participants are navigating the constraints of maximum tension and the relationship between tension, angle, and weight. The discussion reflects uncertainty about the necessary mathematical approaches and the assumptions involved in the setup.

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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.

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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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