A student performed this project and the question is: Why would the experimental velocity be higher than the required velocity and the marble still not make the loop?
Thank You
Mary-Jo
Roller Coaster Marbles: How Much Height to Loop the Loop?
Moderators: AmyCowen, kgudger, bfinio, MadelineB, Moderators
Re: Roller Coaster Marbles: How Much Height to Loop the Loop?
Hi Mary-Jo,
Many ways to answer your question but the simplest approach is to first clarify terminology.
The 'experimental' velocity would be the velocity of the marble recorded during a trial. The 'required' velocity is the minimum velocity the marble needs to complete the loop.
It's tautological, but if the marble's not completing the loop the experimental velocity is below the required velocity for that precise experimental setup.
I'm not sure if you or the student are measuring velocity, but it we consider a starting position along a linear, fixed-slope portion of track we'll probably find a region (position) x along this incline where the marble's got about a 50-50 chance of completing the loop. As experimentalists we would hope that the velocity at the bottom of the loop is identical in each trial but we assume that this is not the case since our results vary. Our 50-50 location x is pretty close to this position of critical potential energy, where experimental error will determine whether or not the marble's going to make it through the loop.
At this point we can push the students and hope for insight-- what's different between the trials? In most university laboratory courses this sort of qualitative error analysis is standard.
An example for this case:
The track is not an ideal surface, it's soft and fairly rough. We'd imagine that a precision-machined metal track and a metal 'marble' would have more reproducible results. (If the nature of your question is due to reproducible results.)
Another more visible concept (to keep blaming the track material) is the flexibility of the track. If you or the students notice any deformation or movement of the track during the marble's roll, this movement or deformation is caused by the rolling marble: potential energy (the marble's height) becomes kinetic energy (the marble's speed) but some of that kinetic energy is transferred to the track itself. The more the track wiggles or wobbles or deforms, the more kinetic energy the marble loses to the track. Different parts of the track will certainly absorb different amounts of energy.
Hopefully some of this explanation is helpful,
-John
Many ways to answer your question but the simplest approach is to first clarify terminology.
The 'experimental' velocity would be the velocity of the marble recorded during a trial. The 'required' velocity is the minimum velocity the marble needs to complete the loop.
It's tautological, but if the marble's not completing the loop the experimental velocity is below the required velocity for that precise experimental setup.
I'm not sure if you or the student are measuring velocity, but it we consider a starting position along a linear, fixed-slope portion of track we'll probably find a region (position) x along this incline where the marble's got about a 50-50 chance of completing the loop. As experimentalists we would hope that the velocity at the bottom of the loop is identical in each trial but we assume that this is not the case since our results vary. Our 50-50 location x is pretty close to this position of critical potential energy, where experimental error will determine whether or not the marble's going to make it through the loop.
At this point we can push the students and hope for insight-- what's different between the trials? In most university laboratory courses this sort of qualitative error analysis is standard.
An example for this case:
The track is not an ideal surface, it's soft and fairly rough. We'd imagine that a precision-machined metal track and a metal 'marble' would have more reproducible results. (If the nature of your question is due to reproducible results.)
Another more visible concept (to keep blaming the track material) is the flexibility of the track. If you or the students notice any deformation or movement of the track during the marble's roll, this movement or deformation is caused by the rolling marble: potential energy (the marble's height) becomes kinetic energy (the marble's speed) but some of that kinetic energy is transferred to the track itself. The more the track wiggles or wobbles or deforms, the more kinetic energy the marble loses to the track. Different parts of the track will certainly absorb different amounts of energy.
Hopefully some of this explanation is helpful,
-John