Uncertainty Principle: Missing Target by Typical Distance

In summary, the conversation discusses the uncertainty principle and its potential application to a marble being dropped from a building onto a target. The uncertainty in the position and velocity of the marble is considered, and it is debated whether the principle applies to macroscopic objects like marbles. The conversation ends with a question about the potential flaws in the reasoning behind the application of the principle to marbles.
  • #1
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Can anyone help me on this??

In a contest to drop a marble with mass 30 g from the roof of a building onto a small target 50 m below. From uncertainty principle considerations, what is the typical distance by which you will miss the target, given that you aim with the highest possible accuracy? Ignore wind and air resistance.

[Hint: Let x be the coordinate in the horizontal direction. You should realize that the uncertainty in the position x of the marble when it reaches the ground depends on both the initial uncertainty in the position xi, and the initial uncertainty in the speed vx.]
 
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  • #2
Let the initial position x0 lie in the interval:
[-dx,dx]

Let the initial velocity v0 lie in the interval:
[-dv,dv]

Now use the ordinary kinematic equations to figure out the extreme values of x(t) and v(t) when the marble hits the target.
 
  • #3
Would the uncertainty principle apply to a marble?

I was always told that it applied to sub-atomic particles. Even atoms were supposed to obey semi-classical formula in my education.
 
  • #4
I've had a longer think about this question (and I haven't done any active physics for years, please forgive the poorly articulated arguement) but I would expect the following:

A particle of uncertainty dX has 2/3 chance of being in the region
x +/- dx.

Two particles each with an uncertainty of dx in a system (ignoring the interactions) should have a centre with a lower uncertainty. Even if both particles are outside the 2/3 probability, if one is on the extreme left and one on the extreme right, this would cancel.

So a mole of particles(or say 10^23) should have a centre with almost no uncertainty even without taking into account the structure of the substance.

I reason that the same is true of particle momenta.

I think this reasoning is wrong because you are all brilliant and I'm useless (and the marble question sounds like a formal one). But why?

Sorry this post was put together at lunch in a cafe. I usally have time to make a proper go of it.
 

1. What is the Uncertainty Principle?

The Uncertainty Principle is a fundamental principle in quantum mechanics which states that it is impossible to simultaneously measure the position and momentum of a particle with absolute precision. This means that there will always be some level of uncertainty in the measurements of these two quantities.

2. How does the Uncertainty Principle affect the Missing Target by Typical Distance?

The Uncertainty Principle plays a role in the Missing Target by Typical Distance because it introduces a level of uncertainty in the position of a particle. This means that even if the target is aimed at with precision, there is a chance that the particle will not be at that exact position due to the uncertainty in its position.

3. Can the Uncertainty Principle be overcome?

No, the Uncertainty Principle is a fundamental principle in quantum mechanics and cannot be overcome. It is a consequence of the wave-particle duality of particles at the quantum level.

4. How does the Uncertainty Principle impact scientific experiments?

The Uncertainty Principle has a significant impact on scientific experiments, particularly in the field of quantum mechanics. It means that scientists must take into account the uncertainty in their measurements and adjust their experimental setups accordingly. It also limits the precision with which certain quantities can be measured.

5. Is the Uncertainty Principle still relevant today?

Yes, the Uncertainty Principle is still a fundamental principle in quantum mechanics and is widely accepted by the scientific community. It continues to be a crucial aspect of understanding the behavior of particles at the quantum level and has implications in various fields, including physics, chemistry, and engineering.

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