Vertical Roller Belt Assembly: Understanding F = S1-S2

[TSN79]

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

$$F=S_1-S_2$$

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

$$F=S_1+S_2$$

since the two S forces would take up half of the force F each. Why is it not so?

 

[brewnog]

Pass. Typo?

 

[TSN79]

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?

 

[brewnog]

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?

 

[TSN79]

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?

 

[Danger]

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?

 

[Q_Goest]

A belt can only be in tension, so the belt on either side of the roller can only produce an upward force.