Wheel on an Angled Belt

[jitspoe]

Ok, this is a variant of KnacK's little thread, here: http://dpball.com/forums/index.php?topic=2761.0

Say we have a belt or treadmill placed at an angle: 45 degrees for simplicity.  Now we place a wheel on it and set up some sensors to monitor the wheel.  If the wheel starts to roll down, the speed of the treadmill is increased to counteract it, such that the wheel maintains its position.  Will treadmill ever reach a constant speed, or will it have to increase indefinitely?

[medley crew 2]

  i dont wanna think i'm on summer vacation 

but i'd probably say indefinitely, just cuz it seems right, the wheel would always go a little faster because gravity would be pulling it down

[P!nk]

Post removed

[S8NATHOME]

THIS ONE won't take off!!!

I think it would have to continually accelerate.
maybe at half 9.8m/s² or womething ... hell i dunno, i can't remember this stuff.

[Spook]

it wont have to increase indefinately cuz gravity is only so strong but the treadmill would counteract it eventually

[b00nlander]

alright, my opinion:
there will be several things we have to take a look at:
- gravity acceleration will be around 9.81 m/s², all the time
- there is some friction involved, as the wheel has contact with the treadmill, which will remain constant if the surfaces don't change
- there is no air friction involved if the wheel stays in place i think (air friction will, for example, keep stuff from falling at unlimited speeds, as it, at some point, counters the gravity => thats why galileo's experiment only fully works in a vacuum)

well, with all these constants, I'd think the treadmill will have to constantly gain speed as well to counter the (gravity - friction) value.

[KnacK]

To truely calculate the answer, you need to figure the coefficient of drag that the wheel has on the belt.

But since the wheels do exhibit drag they are not frictionless, , so yes, the belt will have to continuouslyt increase in speed to keep the wheel in stationary position.

[S8NSSON]

I can't quite remember all that physics stuff I learned, but we have kenetic and potential energy in there somewhere. If the wheel is held at the center of the conveyor, by the conveyor, the wheel will constantly be gaining potential energy from gravity and therefore the conveyor will have to continually accelerate to counter act this.

Maybe the wheel can't be held up at all?

[b00nlander]

well, actually there is another point we have to take into consideration I think:
as any kind of materia increases in speed, its weight will increase. when it reaches light speed, it's weight is like infinite. so any kind of materia cannot be faster (and practically not close to) light speed, so at one point, all this would end due to these limitations

[jitspoe]

I thought about that, but you have to keep in mind that the surface of the wheel is going to be moving at about the same speed as the surface of the belt, so they may both be impacted equally.

Of course, in reality, no wheel or treadmill would hold up at speeds anywhere close to the speed of light.  Also, as the speed increases, any little imperfection would likely send the wheel flying.  It would be difficult to test this outside of a computer simulation.

[Spook]

but we are gonna try lol