- #1
tadietz
- 14
- 0
I have looked around several internet Physics sites and information sources, and even asked questions here and in other places, and can't seem to find answers to my questions about a thought experiment I came up with:
Think about three similar cases: A ball, a solid cylinder, and a hollow cylinder, all with identical mass, rolling individually down an inclined conveyor belt rotating in an 'uphill' direction. Assume there is a sufficient coefficient of friction (CoF) between the objects and the belt to have them roll without sliding and that the conveyor belt's motor speed can be adjusted. Some questions about the system described come to mind:
1) Will the motor driving the conveyor belt do less work in an inclined vs a horizontal position to drive each object to some specified (> 0) rotational speed if the objects are placed on it with initial rotational speed = 0?
My intuition says yes, because an object rolling down a fixed ramp acquires its rotation only from gravity acting on it, and in this scenario, that same force is present and acting on the objects, in addition to the rotation being imparted to them by the conveyor belt's movement.
So, if this is correct, are there differences in the amount of work required by the motor to get each of the differing types of objects (ball, solid cylinder, and hollow cylinder) to the same rotational speed? That is, due to the fact that each object has a different moment of inertia and would accelerate down a stationary ramp at different speeds, does this have an analogous effect in this scenario and cause differing amounts of work to be required of the motor in order to get the objects to a specified rotational speed?
2) Next, is it possible to drive the above described system (regardless of the answer to question #1) to an equilibrium state, i.e., a point where each object would appear stationary with respect to its position on the inclined rotating belt from the perspective of a stationary observer viewing the system?
Again, intuitively it would seem possible, since even an object falling straight down reaches a terminal velocity, i.e., where the drag of air acting on the falling object counters its acceleration due to gravity until a constant speed is reached - at least in a non-vacuum. In my scenario, the drag would mostly be due to the CoF between the objects and the belt, while the acceleration to be offset would be the reduced rate of acceleration due to gravity
acting on the objects on an incline (standard ball-on-ramp calculations apply here, I am guessing, to calculate this rate of acceleration).
As with question #1, if my intuition is correct and an equilibrium can be reached, I am curious if there would be any advantage in terms of object shape to lessen the amount of work required to drive the system to equilibrium.
I hope my descriptions and analogies are sufficiently clear. What I would like to be able to come up with (assuming the answer to question 2 is 'Yes') is an equation that accurately describes the ball/inclined conveyor system which allows me to predict equilibrium states with differing conveyor inclines and speeds, ball sizes and masses, CoFs, etc., so that multiple combinations of factors that result in equilibrium states can be predicted.
Thanks for any thoughts on this.
Think about three similar cases: A ball, a solid cylinder, and a hollow cylinder, all with identical mass, rolling individually down an inclined conveyor belt rotating in an 'uphill' direction. Assume there is a sufficient coefficient of friction (CoF) between the objects and the belt to have them roll without sliding and that the conveyor belt's motor speed can be adjusted. Some questions about the system described come to mind:
1) Will the motor driving the conveyor belt do less work in an inclined vs a horizontal position to drive each object to some specified (> 0) rotational speed if the objects are placed on it with initial rotational speed = 0?
My intuition says yes, because an object rolling down a fixed ramp acquires its rotation only from gravity acting on it, and in this scenario, that same force is present and acting on the objects, in addition to the rotation being imparted to them by the conveyor belt's movement.
So, if this is correct, are there differences in the amount of work required by the motor to get each of the differing types of objects (ball, solid cylinder, and hollow cylinder) to the same rotational speed? That is, due to the fact that each object has a different moment of inertia and would accelerate down a stationary ramp at different speeds, does this have an analogous effect in this scenario and cause differing amounts of work to be required of the motor in order to get the objects to a specified rotational speed?
2) Next, is it possible to drive the above described system (regardless of the answer to question #1) to an equilibrium state, i.e., a point where each object would appear stationary with respect to its position on the inclined rotating belt from the perspective of a stationary observer viewing the system?
Again, intuitively it would seem possible, since even an object falling straight down reaches a terminal velocity, i.e., where the drag of air acting on the falling object counters its acceleration due to gravity until a constant speed is reached - at least in a non-vacuum. In my scenario, the drag would mostly be due to the CoF between the objects and the belt, while the acceleration to be offset would be the reduced rate of acceleration due to gravity
acting on the objects on an incline (standard ball-on-ramp calculations apply here, I am guessing, to calculate this rate of acceleration).
As with question #1, if my intuition is correct and an equilibrium can be reached, I am curious if there would be any advantage in terms of object shape to lessen the amount of work required to drive the system to equilibrium.
I hope my descriptions and analogies are sufficiently clear. What I would like to be able to come up with (assuming the answer to question 2 is 'Yes') is an equation that accurately describes the ball/inclined conveyor system which allows me to predict equilibrium states with differing conveyor inclines and speeds, ball sizes and masses, CoFs, etc., so that multiple combinations of factors that result in equilibrium states can be predicted.
Thanks for any thoughts on this.