Physics of a TreadWheel [Abstract Concept?]

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Discussion Overview

The discussion revolves around the physics of a tread wheel crane, an ancient lifting device, focusing on the mechanics involved in determining the maximum weight that can be lifted based on given parameters such as radii, weight of the user, and their position relative to the center of the circles. The scope includes mathematical reasoning and conceptual clarification related to forces and motion in this context.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant outlines the problem involving a tread wheel crane, specifying the dimensions and weight of the user, and seeks to determine the maximum weight that can be lifted.
  • Another participant notes that the equation v^2/r is typically associated with centripetal acceleration and suggests that the focus should be on the tangential force at the radius of the smaller circle.
  • A subsequent reply acknowledges the need to consider tangential force but expresses confusion over the absence of mass and acceleration in the context of the problem, questioning the validity of the approach.
  • Another participant reiterates the importance of the weight to be lifted, emphasizing that it is attached to the radius of the inner wheel, yet also reflects on the lack of clarity regarding mass and acceleration in the scenario.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correct approach to the problem, with some acknowledging the need for clarity on mass and acceleration while others focus on the tangential forces involved. No consensus is reached on the method to solve the problem or the assumptions that should be made.

Contextual Notes

There are limitations in the discussion regarding the assumptions about mass and acceleration, as well as the definitions of forces in this specific context. The participants do not resolve these issues, leaving the mathematical steps and their implications open for further exploration.

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Homework Statement


[EDIT] Cleaned up the problem.

A tread wheel crane is an ancient device used to lift heavy objects. It consists of a large circle (like a hamster wheel) for a person to walk inside. The large circle connects to the middle where there is a small circle that is attached a rope that goes over a pulley and hooks onto some mass.
http://www.lowtechmagazine.com/2010/03/history-of-human-powered-cranes.html

Givens:
Outer circle radius = 6m
Inner circle radius = 0.5m
My weight: 500N
My speed: unknown.
I stand 1.5m away from the center of both circles

What is the maximum weight I can lift?

Homework Equations


F = (m)(v^2)/r
a(radial) = (v^2)/r
a(radial) = (r)(w^2)
v(tang) = (r)(w)

The Attempt at a Solution


I draw the two circles and placd a dot 1.2m from the center on the edge of the outer circle. The distance from the edge to the center is the radius of the big circle.

You can work out that the tangential force is mgsin(theta) given the geometry. Similarily, you can get a force directed outward mgcos(theta)

I'm thinking that F(Radial) is equal to F(outward). But I also thought perhaps you can solve v(tangential) given the tangent force...

But going ahead with the F(Radial) thing,

F(radial) = F(outward)
500cos(theta) = m(v^2)/r

That is where I was able to get to, because I do not know what mass is in this context. Nothing is really spinning around. Maybe my whole approach is wrong. I would greatly appreciate insight and help!
 
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v^2/r is normally associated with centripetal acceleration. What is wanted in this case is the tangental force at the radius of the small circle.
 
Yeah, I figured that after I thought about it a lot.

So F = ma, and we have the tangental force at the radius of the bigger circle.

But f = ma, and once again, we don't have m and we shouldn't even have a. The circle should not be accelerating. The angular velocity anyway.
 
012anonymousx said:
But f = ma, and once again, we don't have m and we shouldn't even have a.
You have the weight that is supposed to be lifted by a rope attached at the radius of the inner wheel.
 

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