Uncertainty principle and ice pick

[indigojoker]

I need to estimate the amount of time that an ice pick can be balanced at it's tip and the only limitation is set by the Heisenberg uncertainty principle. I assume the tip is sharp and the surface that the tip rests on is hard. I can also assume values of dimensions and weight as long as the this does not change the general order of magnitude of the result. The result must also be in seconds.

I really have no clue where to start. Someone throw me a bone

 

[indigojoker]

i was thinking something like this:

mass of ice pick $$m=0.5 kg$$
the tip of the ice pick is about $$\Delta x = 1x10^{-3} m$$

plug into uncertainty principle:
$$\Delta x \Delta p >= \frac{\hbar }{2}$$
$$\Delta v >= \frac{\hbar}{2 (1x10^{-3} m)(0.5 kg)}$$
$$\Delta v >= 1.05457148 x 10^{-31} m/s$$

then i can estimate a distance that the pen has to move for it to fall and then divide that by the velocity above?

not sure if I'm on the right path, any help would be greatly appreciated :)