Identifying the Gold & Titanium Balls

  • Context: High School 
  • Thread starter Thread starter Sakha
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    Balls Gold Titanium
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Discussion Overview

The discussion revolves around identifying two identical balls, one hollow gold and the other solid titanium, without using measurement devices or damaging them. Participants explore various methods and reasoning related to physical properties, density, and material characteristics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants suggest knocking the balls to determine which is hollow, but this is challenged by the anti-acoustic properties of the paint.
  • Dropping the balls in water is proposed, but participants note that both have the same mass and volume, leading to the same buoyancy.
  • There are discussions about removing the paint, but this is deemed damaging and not allowed.
  • Some participants mention the concept of density and how the gold ball would displace more water, though this is countered by the same mass argument.
  • One participant discusses the trajectory of the balls when shot from a cannon, suggesting that the hollow gold ball would not fly steadily due to its structure.
  • Another participant introduces the idea of using magnetic properties, noting that titanium is paramagnetic and gold is diamagnetic, but questions arise about the use of measurement devices in this context.
  • There are suggestions to scratch the balls with a copper stylus to differentiate them based on hardness, but this is also challenged as potentially damaging.
  • Some participants argue about the moment of inertia, suggesting that the hollow ball would behave differently when spun compared to the solid ball.

Areas of Agreement / Disagreement

Participants express multiple competing views on how to identify the balls, with no consensus reached on a definitive method. Disagreements arise over the validity of proposed methods and the interpretation of the rules set by the original post.

Contextual Notes

Participants note limitations regarding the use of measurement devices and the implications of damaging the balls, which complicates the proposed solutions. The discussion remains open-ended with various hypotheses and methods being explored.

  • #31
LowlyPion said:
use another magnet to detect which one exhibits an attractive force.
That would be a measurement device, albeit a simple one, making a measurement, albeit a simple one.
 
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  • #32
Alternatively you can use a penny or a copper stylus and try to scratch it.

The copper is harder than gold but not as hard as titanium.
 
  • #33
DaveC426913 said:
That would be a measurement device, albeit a simple one, making a measurement, albeit a simple one.

I would claim that it is detection, not measurement. And if detection is not allowed ... then what is?
 
  • #34
LowlyPion said:
Alternatively you can use a penny or a copper stylus and try to scratch it.

The copper is harder than gold but not as hard as titanium.
PLEASE READ THE CRITERIA BEFORE CONTINUALLY OFFERING INVALID RESPONSES.
- both are covered with a black paint that is anti reflective, heat/electricity insulator.
- You can't use any measurement device,
- nor hitting, damaging or breaking the ball
 
  • #35
LowlyPion said:
I would claim that it is detection, not measurement. And if detection is not allowed ... then what is?
It is detection with a device. There is a naked eye obvious way of telling the difference, (if you know what do with the ball :wink:)...
 
  • #36
DaveC426913 said:
PLEASE READ THE CRITERIA BEFORE CONTINUALLY OFFERING INVALID RESPONSES.
- both are covered with a black paint that is anti reflective, heat/electricity insulator.
- You can't use any measurement device,
- nor hitting, damaging or breaking the ball

Ohhh. So grumpy.

DaveC426913 said:
It is detection with a device. There is a naked eye obvious way of telling the difference, (if you know what do with the ball :wink:)...

I still think a magnet is not a measuring device if you are testing merely for a qualitative property of the material. The paint mentioned in the OP is not magnetically reflective after all.

But that said I'd say you can also exploit the difference in the moment of inertia. A shell ball will have a higher moment than a solid ball. You can spin them and the gold ball will either spin slower for the same torque or longer if you get them spinning at the same speed. There's about a 50% difference in the moments.
 
  • #37
LowlyPion said:
Ohhh. So grumpy.



I still think a magnet is not a measuring device if you are testing merely for a qualitative property of the material. The paint mentioned in the OP is not magnetically reflective after all.

But that said I'd say you can also exploit the difference in the moment of inertia. A shell ball will have a higher moment than a solid ball. You can spin them and the gold ball will either spin slower for the same torque or longer if you get them spinning at the same speed. There's about a 50% difference in the moments.

See post #4.
 
  • #38
lisab said:
See post #4.

It just says spoiler.

I've already been accused of not reading the OP carefully enough.
 
  • #39
LowlyPion said:
It just says spoiler.

I've already been accused of not reading the OP carefully enough.

Ah - run your cursor over the text box under 'Spoiler.'

You've read the OP perfectly well :wink: !
 
  • #40
lisab said:
Ah - run your cursor over the text box under 'Spoiler.'

LOL. Thanks. I didn't know what that was.

Now there is a puzzle I didn't get.

Thanks for the tip.

Oh and good answer. I like yours better.
 
  • #41
Isn't the ramp a device for measuring rotational inertia? :-p
 
  • #42
Hurkyl said:
Isn't the ramp a device for measuring rotational inertia? :-p
Nope. Your eyes are all that is needed to see the difference. There was no restriction on what you could do with the ball to cause the difference.
 
  • #43
LowlyPion said:
I've already been accused of not reading the OP carefully enough.
:wink:
 
  • #44
DaveC426913 said:
Nope. Your eyes are all that is needed to see the difference. There was no restriction on what you could do with the ball to cause the difference.
My eyes are all I need if I set them down next to a strong magnet too. :-p (Or if I place the balls in any sort of object one might label as a 'measuring device')
 
  • #45
DaveC426913 said:
Nope. Your eyes are all that is needed to see the difference. There was no restriction on what you could do with the ball to cause the difference.

I don't know ...

I think he's got a point. A ramp is as much a device that detects a property of the ball (moment of inertia) as a magnet (paramagnetism).

I'd say in the future the OP would want to insure that the statement would say something like no chemical, electrical or magnetic property of the material can be used to differentiate. ... You know for those of us so easily misled.
 
  • #46
LowlyPion said:
I don't know ...

I think he's got a point. A ramp is as much a device that detects a property of the ball (moment of inertia) as a magnet (paramagnetism).
Granted, it's a hazy line. You guys are pretty resourceful.
 
  • #47
DaveC426913 said:
Granted, it's a hazy line. You guys are pretty resourceful.

HAZY?

Progress is slow.
 
  • #48
LowlyPion said:
HAZY?

Progress is slow.
OK, well, how about:

I'm at a loss to see a difference between a ramp being used to cause two objects to move in visibly distinguishable ways and a magnet being used to cause two objects to move in visibly distinguishable ways.

So, I must concede the point.


(Of course, I'm not out yet. I'll bet there is a way to show the angular momentum effect without needing a ramp. Thus, all devices could be verboten.)
 
  • #49
DaveC426913 said:
I'll bet there is a way to show the angular momentum effect without needing a ramp. Thus, all devices could be verboten.

In that regard spinning them by hand, should work. The gold will feel "heavier" to spin - resist spinning by about 50%. (I checked the Hyperphysics calculator and it shows a ration of about 20:33 between a solid and a shell sphere.)

Oh but then the hand might be seen as a device ...

We'll have to just decide to live with the imprecision.

But I still think lisab's solution is the best.
 
  • #50
LowlyPion said:
I'd say in the future the OP would want to insure that the statement would say something like no chemical, electrical or magnetic property of the material can be used to differentiate. ... You know for those of us so easily misled.
I'll try next time :rolleyes:
 
  • #51
Sakha said:
You have 2 balls. Both are identical in size and mass, but one is made of gold and is hollow,the other is not hollow and made from titanium. Find out which is which ball, and let's say both are covered with a black paint that is anti reflective, heat/electricity insulator. You can't use any measurement device, nor hitting, damaging or breaking the ball..[i/]

P.S: There's a really simple way.


take them to a goldsmith. tell him that he can have one sphere. you'll sell it to him for half the price of it's weight in gold.
 
  • #52
Phrak said:
take them to a goldsmith. tell him that he can have one sphere. you'll sell it to him for half the price of it's weight in gold.

And how can you say which is the gold ball by doing that?
 
  • #53
Sakha said:
And how can you say which is the gold ball by doing that?

I'll bet my gold ball against your titanium ball i walk away with the titanium.

no, wait a minute. I sold the gold ball.

but then again. If you think its gold, want to buy it?
 
  • #54
LowlyPion said:
In that regard spinning them by hand, should work. The gold will feel "heavier" to spin - resist spinning by about 50%. (I checked the Hyperphysics calculator and it shows a ration of about 20:33 between a solid and a shell sphere.)

Oh but then the hand might be seen as a device ...

No. I (on behalf of the OP :redface:) said that your eyes were not considered a device. One can presume that using one's body is not "making use of a device".
 
  • #55
LowlyPion said:
In that regard spinning them by hand, should work. The gold will feel "heavier" to spin - resist spinning by about 50%. (I checked the Hyperphysics calculator and it shows a ration of about 20:33 between a solid and a shell sphere.)

Oh but then the hand might be seen as a device ...

1] Giving the balls the same amount of force, one ball will spin slower than the other. This will be visually discernable without need for measurement.

2] I (on behalf of the OP :redface:) said that your eyes were not considered a device. One can presume that using one's body, such as one's hand, is not "making use of a device".
 
  • #56
Before getting into too much detail about that and inventing paint that practically works as a force field, how about generalizing the problem like:

You have two balls A and B made from different metals of the same size. The metals only differ in volume, so that although one of the balls is hollow and one is solid they both weigh the same. How do you tell the two apart?

Or maybe that is giving away the starting point as it only gives one information?
 
  • #57
The most austere method I can think of is to bounce the two balls off of each other, in an off-center impact.
 
  • #58
Phrak said:
The most austere method I can think of is to bounce the two balls off of each other, in an off-center impact.
What would that accomplish?
 
  • #59
Re: off-center impact of one ball on another.
DaveC426913 said:
What would that accomplish?

All impacts are not perfectly elastic. The angular momentum imparted to one ball will be equal and opposite the angular momentum imparted to the other. The ball with the least angular velocity is hollow.
 
  • #60
Phrak said:
Re: off-center impact of one ball on another.


All impacts are not perfectly elastic. The angular momentum imparted to one ball will be equal and opposite the angular momentum imparted to the other. The ball with the least angular velocity is hollow.
Oh, OK, a riff on the angular momentum solution.
 

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