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Name: Brian
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 2001-2002


Question:
I teach high school physics. The ring and disk (equal mass and radius) "racing" down the ramp demonstration is a favorite one of my because it is hard for the students to predict but one that is easily understood once I explain it. My question is this: While it is true that the disk will make it down the ramp first, if we allow them both to continue rolling along a flat surface (carpet), which will come to rest first? I think they will both travel the same distance because they each start with the same amount of potential energy. Am I right or am I missing something? I've tried it buy the ring and/or disk never goes straight until stopping. Thanks!


Replies:
I would not know which one would go faster down the ramp either!!! The problem with rolling either object on a carpet is that they will be subject to more or less random side forces due to the texture of the carpet. And of course once the disc or sphere gets a slight sideways direction the trajectory is going to become random. You might try a smooth surface, or if they go too far to be practical, use a sheet of self adhesive wall paper or shelf paper and the tackiness of the adhesive will shorten the path of both. In fact, this "rolling ball" or "rolling cylinder" method is used in reverse to get some idea of the tackiness of adhesives. The ball//cylinder rolls down a ramp at a certain angle, and then across a horizontal length of the adhesive. The higher the "tack" of the adhesive the shorter distance the ball/cylinder will roll. And you record the number of cm.

Vince Calder


Absent friction, they would both roll forever on a flat surface, so the question is "does friction care how momentum is divvied up between linear and angular?" I suppose it does, in some complicated way that would require details about the carpet to understand, and certainly friction with air increases with speed. On the whole, though, I would say there is little of fundamental interest in the distances these objects travel.

Tim Mooney


Brian,

I would not be so quick to make a decision on this one. When slowing down, the force is no longer constant or conservative. Air resistance depends on speed. Once on the floor, the disk is moving faster, so the disk initially experiences a greater air resistance force than does the ring. In most cases, faster objects are affected more by air resistance. I would not make a definite judgement until I tried it. If you want the objects to roll straight, use a long metal tube and a wooden cylinder of the same length and mass. A solid plastic cylinder may also work. If the low-density cylinder is too light, insert metal pegs near the center. If the metal tube is too light, add a thin layer of wax on the inside. I would recommend a length of at least twice the diameter.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


If the frictional force is proportional to the mass of the disk and ring, they should travel the same distance before stopping.

This is because, as you say, they start with the same amount of potential energy (mgh) if they have the same mass and give up that energy while travelling a distance d where mgh = umgd. The frictional force is umg where u is the coefficient of friction.

To a first approximation the frictional force is proportional to the mass, but it could depend on properties of the carpet and other second order effects.

Best, Dick Plano...



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