playful exercise

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wulsy

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Interesting, thanks for this mandrin.

OK, here's my clueless thought process:

They all have identical speeds when they reach the hook.

Heavier objects are harder to accelerate according to the principle of inertia (resistance to change of state directly proportional to mass) therefore , B would be the slowest. Also, a = F/m. So a higher mass when F remains constant would result in less acceleration.

Then A would be next slowest because in C the mass is "effectively" lighter than in A. Although I'm not sure about that, as there are 2 weights (double the weight) operating from 2 different radii so I'm totally confused on this one and it could be the other way round. The weight and radius change could also cancel each other out. No idea...

Fastest would be D because the radius is being shortened and a = "v-squared"/radius.

So I'll stettle for D (fastest), C & A the same, B (slowest).

Realising my complete incompetence, I look forward to the answer and perhaps an explanation for simpletons like myself.
 
ZAP

ZAP

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BertramSterling said:
Going to guess that A, B and C have the same velocity, but D is faster
Click to expand...

Agree with this. They will all have the same velocity initially with the vertical fall and then the basic determining factor in the period of the swing would be the radius of the pendulum. Did that sound smart? lol.
 
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leon

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D, then A&B are equal, then C (from simple energy balance)

C is mathematically more complicated (I had to get a pen & paper) and depends on the ratio of masses and where m2 is placed. In the limit that m2=0 or is placed at either end, then C would also be equal.
 
mandrin

mandrin

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leon said:
D, then A&B are equal, then C (from simple energy balance)

C is mathematically more complicated (I had to get a pen & paper) and depends on the ratio of masses and where m2 is placed. In the limit that m2=0 or is placed at either end, then C would also be equal.
Click to expand...
leon,

Not only on the green but right into the hole. :cool:
 
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wulsy

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Well done leon!

mandrin, looking forward to your explanation. It was a nice little puzzle.

I shudder to think how many formulii and principles were involved in this simple model. It makes you realise that the golf swing with its infinitely higher complexity is surely almost impossible to truly understand.

In your model you shorten the radius by shortening "the shaft". There has been much talk about shortening of the radius in the golf swing. By how much is it shortened and which radius is actually shortened? In the case of the golf swing the shaft cannot be shortened ;), so clearly by shortening this "other" radius you are having a similar effect. How does the connection between these two radii (shaft constant length, "other" radius shortening) function?
 
mandrin

mandrin

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wulsy said:
mandrin, looking forward to your explanation. It was a nice little puzzle.

I shudder to think how many formulii and principles were involved in this simple model. It makes you realise that the golf swing with its infinitely higher complexity is surely almost impossible to truly understand.

In your model you shorten the radius by shortening "the shaft". There has been much talk about shortening of the radius in the golf swing. By how much is it shortened and which radius is actually shortened? In the case of the golf swing the shaft cannot be shortened ;), so clearly by shortening this "other" radius you are having a similar effect. How does the connection between these two radii (shaft constant length, "other" radius shortening) function?
Click to expand...
wulsy,

It will be explained in detail. I have to be a bit careful with some around all too happy to exploit any tiny mistake to declare it all immediately 'junk science'. ;)

Your questions about the swing radius are very interesting and right on the dot. It is where I want to go in the near future. So just bear with me and it will be forthcoming before long.
 
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leon

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Mandarin, glad to hear this is going somewhere, although it was fun as a standalone exercise.

Wulsy, I have no internet science reputation to worry about, so while we wait for Mandarin to do it properly, here is my take.

The basic premise is conservation of energy, so all potential energy is converted to kinetic energy. Mathematically:

mgh = 1/2 mv^2

Mass is on both sides so cancels and you can rearrange to get:

v = sqrt(2gh)

So mass makes no difference, hence A & B are identical. The loss in height for D is least, hence D has lowest velocity. C is more complicated, but you can sum the total energy of m1 and m2 and use the fact that the rotational speed of both masses is the same. At this point I resorted to pen & paper.

I think the interesting part is that D seems contrary to 'shortening the radius' as people understand it. But remember that nobody since Earnest Jones swings a mass on a string, and even he didn't swing it around some intermediate pin! The key is that to the radius doesn't really reduce, it just moves up. And to do that, you have to add (a lot of)
force.

I may suck at golf, but I can add up. I'd trade though!
 
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