Real World Lifting Problem: path of 4000mm cable

[mmilez912]

Hi, this is my first post. Hopefully I am in the right area. I am concerned that this may reach over into calculus but I'm hoping not.

I have a real world problem where I am trying to calculate the path a cable will take when lifting an item given certain dimensions. Basically the cable will have a starting (attach) point, and then travel past an edge with a given distance from center line in the y-dimension and z-dimension. I would like to calculate the x-dimension value that creates the straightest line possible (most natural path). The length of the cable is 4000mm. So in the following problem, the calculated x-dimension in P₂ will affect the lifting point (z-dimension of P₃)

I have tried using the distance formula and could solve for 1 variable or the other. I know to solve for 2 variables you must have 2 equations. I am just struggling to figure out what the second equation would be and hoping it doesn't involve calculus because I haven't taken it in like 15 years. lol.

Please review the following problem, diagram, and my shown work and any help would be greatly appreciated.

 

[Deleted member 4993]

Hi, this is my first post. Hopefully I am in the right area. I am concerned that this may reach over into calculus but I'm hoping not.

I have a real world problem where I am trying to calculate the path a cable will take when lifting an item given certain dimensions. Basically the cable will have a starting (attach) point, and then travel past an edge with a given distance from center line in the y-dimension and z-dimension. I would like to calculate the x-dimension value that creates the straightest line possible (most natural path). The length of the cable is 4000mm. So in the following problem, the calculated x-dimension in P₂ will affect the lifting point (z-dimension of P₃)

I have tried using the distance formula and could solve for 1 variable or the other. I know to solve for 2 variables you must have 2 equations. I am just struggling to figure out what the second equation would be and hoping it doesn't involve calculus because I haven't taken it in like 15 years. lol.

Please review the following problem, diagram, and my shown work and any help would be greatly appreciated.

View attachment 10441

Your image too small and fuzzy for me decipher. Can you type in the text part?

 

[mmilez912]

Sorry, Hopefully it shows up larger this time. If not I will try to type it all out.

Thank you.

 

[mmilez912]

Checking In...

Just checking in to see if anyone has any thoughts/ideas of how to move forward with this problem. Any help would be GREATLY appreciated. Thank you!!!