Vertical Roller Belt Assembly: Understanding F = S1-S2

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Discussion Overview

The discussion revolves around the forces acting on a vertical roller belt assembly, specifically examining the equation F = S1 - S2, where F is the force acting on the lowest roller and S1 and S2 are the reaction forces from the belt. Participants explore the implications of the belt's design, including the presence of shovels or buckets that pick up sand, and the nature of forces involved in this system.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions the equation F = S1 - S2, suggesting that it should be F = S1 + S2, based on the assumption that the forces would be equally distributed.
  • Another participant introduces the concept of shovels on the belt, prompting a discussion about their potential impact on the forces involved.
  • A participant expresses confusion about the direction of forces, suggesting that the force on the bottom roller should be upward, as its role is to support the belt.
  • One participant asserts that the belt can only be in tension, indicating that the forces produced by the belt on either side of the roller must be upward.
  • A participant reflects on the belt's resistance to movement, proposing that this resistance influences the direction of the reaction forces.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct interpretation of the forces involved or the validity of the equation F = S1 - S2. Multiple competing views remain regarding the nature of the forces acting on the rollers and the effect of the belt's design.

Contextual Notes

There are unresolved assumptions regarding the mechanics of the belt system, including the role of the buckets and the nature of the forces acting on the rollers. The discussion reflects varying levels of understanding among participants.

Who May Find This Useful

Individuals interested in mechanical systems, conveyor belt dynamics, or those studying forces in engineering contexts may find this discussion relevant.

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Two rollers have a belt that goes between them, like a conveyerbelt. The assembly stands vertical. The lowest of the rolls have a force that acts on its center, and downwards. My book says that this force F can be written as

[tex]F=S_1-S_2[/tex]

where S are the forces that the belt produces as a reaction to F. I would have guessed

[tex]F=S_1+S_2[/tex]

since the two S forces would take up half of the force F each. Why is it not so?
 
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Pass. Typo?
 
Well, there are small "shovels" on the belt that picks up sand on the way up and then they come down again on the other side to pick up more. Does this make a difference?
 
Aha, I was waiting for the extra information!

Sounds a tad like homework. Ask yourself what the purpose of such a belt is. Do you think having these buckets makes a difference?
 
First, it's not "homework", I have the whole solution here, but I just don't see why there is a minus and not a pluss sign in the equation that's all. I'm thinking that if the belt had a "mind of its own" it wouldn't want to move. So on the side where it goes up, it tries to resist and so S points downward. On the other side the belt goes down, and so it also tries to resist this movement and so S point upwards here. Am I on to something at all with this thought?
 
Maybe it's just because I have no particular knowledge in this area, and anything that vaguely resembles a formula scares the hell out of me, but one thing strikes me as a little odd. As nearly as my common sense tells me, the force on the bottom roller should be upward since its only purpose is to hold the bottom of the belt down. There should also, I think, be a lateral force when the buckets dig into the sand and drag it sideways before heading up. Am I missing something here?
 
A belt can only be in tension, so the belt on either side of the roller can only produce an upward force.
 

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