Some brain teaser for the scientific-minded

[henry1]

If I have an adhesive that holds a 1 cm x 1 cm tile onto the ceiling, will the same adhesive hold a similar tile 2 m x 2 m onto the same ceiling? If not, why not?

Before you say it's heavier, consider that the adhesive is providing the same force per unit area for both tiles, and the force of gravity per unit area for both tiles is also the same...

I asked 2 different AIs this question. One said it was due to imperfections, as if there are no imperfections in the 1 cm x 1 cm tile scenario. The other AI in the end agreed with me because I was relentlessly harassing it!

 

[motorbiking]

The bonding properties of the adhesive will not be uniform. So it would depend on how the adhesive is to be applied and any curing requirement. This is a well known (slightly different) problem for 3D titanium printing for example. As you scale up the build you have to take account of the heat from the print. there will be a scenario where no matter how small the tile you will need more glue and there will be a scenario that no matter much glue applied it will not be strong enough.

 

[henry1]

We all know the large tile won't hold up and we all intuitively say because it's too heavy. But is that really the case?
The bonding property of the adhesive many not be uniform but over a 2 m x 2 m surface, could any irregularity be negligible? It's not as if 25% of the surface won't bond.

 

[simplesteve]

I see two trains of thought to the o.p. :-
Whilst thinking ' no, cos it's too heavy', surely ( for example) 10kg/m2 is the same for 1M as it is for 2 ?
But you can't argue with my second reasoning - ' No, because the adhesive has already been used'. Therefore the SAME adhesive can't be used as it has to be new adhesive !

 

[MNW67]

and the force of gravity per unit area for both tiles is also the same...

I don't think you can actually measure gravity per unit area. But I know what you mean. Presumably, you are referring to the downward force being applied to the adhesive by gravity acting on the mass of the tile.

 

[Mottie]

We all know the large tile won't hold up and we all intuitively say because it's too heavy. But is that really the case?
The bonding property of the adhesive many not be uniform but over a 2 m x 2 m surface, could any irregularity be negligible? It's not as if 25% of the surface won't bond.

So if a steel pin will float on the surface of water, will 1000 pins all joined together also float on water? If not, why not?

 

[Trazor]

Not really a brain teaser....... 1 tile, 1cm x 1cm will hold, therefore 40,000 tiles 1cm x 1cm will also hold when applied randomly.

Now rearrange the 40,000 tiles into your 2M x 2M square, why should they now fall off....?

 

[denso13]

Before you say it's heavier

It is "heavier" in that it has a greater gravitational pull on it, than the small one. The size is immaterial, it is the mass of the whole object that matters. The larger tile will have a greater mass, therefore gravity will affect it more.

 

[motorbiking]

I don't think you can actually measure gravity per unit area. But I know what you mean. Presumably, you are referring to the downward force being applied to the adhesive by gravity acting on the mass of the tile.

Aren’t we able to assume that the mass per meter squared is the same between the two tiles? For the purposes of the exam question.

I think simplesteve’s first point is sound.

The issue is the bonding performance of the glue. It won’t be linear.

 

[MNW67]

So if a steel pin will float on the surface of water, will 1000 pins all joined together also float on water? If not, why not?

It will probably depend on how they are joined. End to end in a massive long line or clumped together.

 

[MNW67]

Aren’t we able to assume that the mass per meter squared is the same between the two tiles? For the purposes of the exam question.

Yes, of course. I was just trying to be a bit more rigorous about the science.

 

[henry1]

So if a steel pin will float on the surface of water, will 1000 pins all joined together also float on water? If not, why not?

a steel pin doesn't float although steel does float if shaped appropriately.

 

[noseall]

So if a steel pin will float on the surface of water

?

 

[MNW67]

?

I'm sensing some tension

But only on the surface.

 

[henry1]

Aren’t we able to assume that the mass per meter squared is the same between the two tiles? For the purposes of the exam question.

I think simplesteve’s first point is sound.

The issue is the bonding performance of the glue. It won’t be linear.

It doesn't have to be linear or non-linear. The adhesive will only act where it is applied, so we could consider it acting only in its tiny 1 cm x 1 cm little square within the large tile. What the adhesive is doing in one corner doesn't affect the adhesive in the other corner as long as both are pulling their weight