Sanity check please -- Load cable swinging outward on a rotating crane

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Homework Help Overview

The discussion revolves around the dynamics of a load cable swinging outward on a rotating crane, focusing on the relationship between various forces and the geometry of the system. The subject area includes concepts from mechanics, specifically centripetal force and rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are examining the equations governing the motion of the load cable, questioning the relationships between the variables involved, and exploring how to simplify the expressions used. There is a focus on the proportionality of certain variables and the implications of the crane's rotation.

Discussion Status

The discussion is active, with participants confirming each other's reasoning and suggesting ways to refine the equations. There is an acknowledgment of a variable that may need to be eliminated from consideration, indicating a productive exploration of the problem.

Contextual Notes

Participants note that certain variables are restricted based on the homework guidelines, which influences their approach to the problem. The geometry of the crane's rotation is also a critical factor in the discussion.

Thickmax
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Homework Statement
Please can my work be sanity checked? I think I'm on the right lines
Relevant Equations
See below
1624914062559.png
So I know

Fcp=-m*w^2*r

So from the equation -m*w^2*r=m*g*tan(theta)

r = r1+r2

so to rewrite

-m*(w^2)*(r1+r2)=m*g*tan(theta)
So
r1+r2=(m*g*tan(theta))/-m*(w^2)

r1=((m*g*tan(theta))/-m*(w^2)) - r2

Am I doing this nearly correct?
 
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Thickmax said:
Am I doing this nearly correct?
Yes, but one of your variables is not in the list of those allowed in the answer. Can you see a way to get rid of it?
 
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Shouldn't ##r_2## be directly proportional to ##\omega^2##?
 
Lnewqban said:
Shouldn't ##r_2## be directly proportional to ##\omega^2##?
No the crane rotates around its base column, the radius of rotation is ##R=r_1+r_2## not just ##r_2##.
 
haruspex said:
Yes, but one of your variables is not in the list of those allowed in the answer. Can you see a way to get rid of it?
I can indeed! m's are overrated! Thank you for the confirmation
 
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