Uncertainty principle and ice pick

In summary, to estimate the amount of time an ice pick can be balanced at its tip, the Heisenberg uncertainty principle can be applied by assuming values for the dimensions and weight. The result must be in seconds and the tip must be sharp and resting on a hard surface. Using the equation \Delta x \Delta p >= \frac{\hbar }{2}, with a mass of 0.5 kg and a tip size of 1x10^{-3} m, the estimated velocity is 1.05457148 x 10^{-31} m/s. Further calculations can be made by estimating the distance the pick needs to move for it to fall and dividing it by the velocity. Additional help may be needed to confirm
  • #1
indigojoker
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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:uhh:
 
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  • #2
i was thinking something like this:

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

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

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 :)
 

1) What is the uncertainty principle?

The uncertainty principle is a fundamental concept in quantum mechanics that states that the position and momentum of a particle cannot both be precisely known at the same time. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2) How does the uncertainty principle relate to an ice pick?

The uncertainty principle applies to all particles, including subatomic particles. In the case of an ice pick, the tip of the pick can be seen as a particle with a position and momentum. Therefore, the uncertainty principle would apply to the ice pick in the same way it applies to any other particle.

3) Can the uncertainty principle be observed in everyday life?

Yes, the uncertainty principle is a fundamental aspect of the behavior of particles and can be observed in many everyday situations. For example, the uncertainty in the position of an electron in an atom leads to the concept of electron orbitals, which determine the chemical properties of elements. However, the effects of the uncertainty principle are typically only noticeable at the subatomic level.

4) How does the uncertainty principle affect our ability to measure things?

The uncertainty principle places a fundamental limit on our ability to measure both the position and momentum of a particle. This means that there will always be some degree of uncertainty in our measurements, no matter how precise our instruments are. The uncertainty principle also plays a role in other areas of measurement, such as time and energy.

5) Is the uncertainty principle a proven concept?

Yes, the uncertainty principle has been extensively tested and confirmed through numerous experiments in quantum mechanics. It is a fundamental concept that is crucial for our understanding of the behavior of particles at the subatomic level. The principle was first proposed by Werner Heisenberg in 1927 and has been validated by various experiments since then.

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