Calculating sand penetration of ice solid from height X

[MattRNR2]

G’day physics forum

This is a purely hypothetical question and my knowledge of physics is rather limited so I’ve no idea if answering it is even possible however here goes:

Imagine a 30cm long timber stick approximately 3mm in diameter that has been placed vertically in an inverted pyramid or conical mold (approximately the size of a ice-cream cone) filled with water and frozen so when removed it is frozen in the middle of a solid block of ice that tapers to a point.

I’m trying to work out at what altitude this object would need to be dropped in order to impact a surface composed of a certain substrate (say sand) and penetrate such that n cm (say 40cm) of the timber post would be exposed above the surface and the block of ice and ‘1m – n cm’ (i.e. 60cm) were buried beneath the surface.

I’m guessing such an equation would require a measure of the substrate density, weight and dimension of the ice and gravitational acceleration.

If anyone out there has any idea how this can be achieved or at the very least whether or not this can be achieved give us a yell.

Regards

MattRNR2

Incidentally there is a beer riding on this so suffice to say I'm taking it pretty seriously

 

[Bystander]

30cm long timber stick

(say 40cm) of the timber post would be exposed above

and ‘1m – n cm’ (i.e. 60cm) were buried beneath the surface.

can be achieved

"Achieved?" Yes, ... BUT ...
Most "bar bets" are rigged. The rigging on this bet may be as simple as stretching the 30 cm stick to 1 meter. If that's just a transcription artifact, sure, there are ways to work out drop heights for what you've described.

 

[mfb]

It will depend on the sand (composition, amount of water, ...), the angle of the ice, the mass of the ice and many other factors.

60 cm sounds very problematic with an ice-cream-cone-shaped object.

 

[Frabjous]

Google "young penetration equations" for a Sandia report. Assuming that the ice remains intact, they should work.

 

[davenn]

Imagine a 30cm long timber stick approximately 3mm in diameter that has been placed vertically in an inverted pyramid or conical mold (approximately the size of a ice-cream cone) filled with water and frozen so when removed it is frozen in the middle of a solid block of ice that tapers to a point.

I’m trying to work out at what altitude this object would need to be dropped in order to impact a surface composed of a certain substrate (say sand) and penetrate such that n cm (say 40cm) of the timber post would be exposed above the surface and the block of ice and ‘1m – n cm’ (i.e. 60cm) were buried beneath the surface.

and your 30cm stick suddenly became 100cm ( 1m) long ??