Rolling, Rolling, Rolling...: Newsletter Challenge (June 2014)

Since we reached the hard bottom of the classic mechanics, it would be interesting to find the maximum theta for a given friction coefficient for which the hollow cylinder still is left behind, eh?

I'm, going to have to GA you. Not because of the detailed stuff, but because you mention a superb utility (GeoGebra). Anyone reading this who has not yet tried that one is a muppet.

A week of family visiting, and my brain is too fired to check all you say (but I have little doubt you are correct). Plenty of stuff on the internet on this specific question, yet few people who could analyze and answer this in their own words.

As mentioned by a few people, some of the value here is in ripping on the question. Just my observation, but if ya can't see the solution to any given problem, it's because you don't understand the question. Ambiguity is very much part of the game in these Newsletter Challenges, but that overall fact holds true in life.

GA because you have made some ace post on this topic, and all worth reading.

Would you please return the photograph of me, naked in the shower, that I accidentally posted ?

Posting OT because, well, it is. Adding a vote will help guide those short on time toward the stuff worth reading. I am still recovering from laughter at the picture of both cylinders in an 'x' shape - brilliant way of getting us all thinking about how we interpret a question.

So according to this math, if one wants to slow down a solid cylinder when rolling down an incline, all one has to do is to hollow out the inside. And I assume that the more it is hollowed out, the slower it will roll.

I think there was a disclaimer "(psst: again, no mention of mass nor radius

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If My MIL breaks wind when going to the loo, will she fall down the staircase quicker or slower (friction and airblast being negligible) ? That may sound glib, but it was a real-life situation. I'd give a decent answer, but the post to which you reply seems to indicate that you might just get ripped by some very detailed explanation.

For what it's worth, that is a good question to ask. The answer probably has no bearing on Galileo/Piza and all that, but a simple comparison would be good to hear. CR4 needs a 'Good/Provocative Question' button.

My money still says (and I have forgotten the question) that whatever cylinder (and it's orientation, straight or otherwise) will hit the bottom at the same time. My reasoning is based upon the ambiguity of the original question.

ROFL! Either the loo is at the very top of the stairs or your MIL was airborne for a time, making it more of a ballistics question (at least in part)? Shock 'n' Awe.

Note that the 'correct answer' redefines the original question to conform to the answer, and so the 'correct answer' is no longer the answer to the original question but to a different question, one asked after the fact.

From the original question: "Assuming the frictional effects are negligible ..."

That word, negligible? What does it mean for something to be negligible?

Now, what supplies the torque that causes these cylinders to rotate? Friction? Ah, but the friction here is negligible, and since it is, so must be the torque. Insignificant, not worth considering.

Yet, these cylinders are rolling. What to do? Realise that one omitted a critical detail in framing the original question, or redefine the question to conform to the 'correct answer' (in the process getting half of the 'correct answer' wrong).

So much for Challenge Questions, ay? This would have made a great trick question, but they didn't capitalise on it. From everyday experience, most everyone would have expected the cylinders to roll and not slide, and would solve the problem accordingly, ignoring this one essential detail. That is what the framer of this question did. In my physics class? I would have docked points for making such an assumption. It is the habit of making these kinds of assumptions that lead to Sloppy Science.

You are quite corect about loo location, though it's a bit late to help me !

Many years ago my Dad gave me a book in which he had written. "Good boooks are one of lifes great p[leadures" (his spelling was rather better than mine). The format may have changed, but the notion is still the same.

"Sloppy Science" - That would be a slamdunker of a good thread. The threat of psudo-science needs taking to hand.

These are my Q's

questions are always posted with enough ambiguity to get some conversation going. That is no bad thing.

I will GA anyone who can explain why, 'Steven and the Romans' may explain this. For many years I has no idea why cowpokes (funny enough in itself) would want to roll dogs across the open plain. Shaddup already, I was a young kid watching the Saturday Matinee at the local 'flix' for a matter of pennies.

My history knowledge is bad, but the Romans did not run steam trains. What kind of perverted act was going on when people rolled dogs down hillsides ? It is too shameful to explain how long it took me to figure that out.

OK, I know the history, but the themetune baffled me.

A gratuitous and useless GA to whoever can tell me which guitarist was in a well know 70's TV series. If The right person guesses the Spaniard maestro (+ show and episode), the photograph will either be scanned or in the mail within 48n hours.

Santana - James at 16?

You are getting closer, but still way off the mark.

To heck with the silly original question, we (mostly europium MK whatewver) have well and truly butcherd it. Come on people, classic 70,s telly and a guitar maestro.

I don`t know the episode number, but I assure you he is in the series. OK, you can all burn me if you think you can . Well worth buying ther boxed series of Kung Fu.

I agree to the solid disk taking the initial lead. The heavier "Pb" unit will overtake the Al unit if the track is long enough to let the force of air resistance to act on the pair.

What if the cylinders are 10 meters in diameter and the ramp 1 cm long? Do the same physics apply?

Assuming no slippage and no external interference, a solid cylinder will always accelerate ahead of a hollow one. It makes no difference what they weigh, what they're made of, how long they are nor their density, as long as it's radially uniform. They can even have very different lengths and radii, but the solid cylinder will always pull ahead (to see why this is so, see Post #88, especially the end. Note that the acceleration depends only on the pull of gravity, the slope angle and a coefficient. For solid cylinders the coefficient is 2/3. For hollow cylinders the coefficient is always less than 2/3.)

"...What if the cylinders are 10 meters in diameter and the ramp 1 cm long?..."

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Depends on a number of factors, some of which still may not have been mentioned in this post...

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What is the angle of the ramp and are they on a horizontal and flat surface? If the angle of the 1 cm. ramps is more than a few degrees, the 10 m. cylinders will never make it further down the ramps than the tops.

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In all cases, assuming the ramps are on horizontal flat surfaces and that that the ramps are simple flat inclined planes, a rolling cylinder will never reach the bottom of the ramp.

Absolutely correct, however, the real point of these challenges is to spur a discussion/conversation. I agree that the holes in this particular challenge are so large that one can validly argue that either or neither cylinder should reach the "bottom" first. I, for one, offers many kudos to this challenge for the in depth analysis of all of the possible interpretations that people have provided on these ambiguities. This discussion has been far more stimulating than a precise, unambiguous challenge with a cut and dry answer. As expected the 'official' answer disregards an opening criteria to achieve the desired result.

Get over it.

IMHO I like this challenge. It made many of us really think.

"Get over it."

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No one made you the boss of me. I'm not going to 'get over it' because there is not 'it' in this case for me to surmount.

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If I gave the impression that I didn't like this challenge, it wasn't intended. I wouldn't keep coming back and commenting if I didn't find it interesting and worth discussing.

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I agree there is a lot missing from the problem, and I also agree that it has lead to a more thorough discussion. I also think there are a number of important factors that haven't been mentioned in the comments yet.

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This problem like all other problems is incompletely described. Being cognizant of the possible effects of the various parameters of consequence for which no information has been given has great utility in life, and not just at calling out the incompleteness of a challenge question.

"... a lot missing from the problem."

Apart from the problem statement's being COMPLETELY misleading about the effect of friction, it nevertheless provides sufficient info to solve the problem, so what's missing?

Consistency? Reality?

same procedure as every year

you are right

and I am quiet