# Uncertainty Principle Homework: Minimal Width of Crack

• asi123
In summary, the conversation is discussing a problem involving a ball being thrown at a crack in the floor and using the uncertainty principle to determine the minimal width of the crack in order for the ball to hit it. The person is also looking for a connection between the uncertainty in velocity and the velocity itself. However, there is some confusion about the problem and its solution.

## Homework Statement

Hey guys.

I have this kid throwing a ball with mass M and from high H.
He is trying to hit a crack in the floor.
I need to show that in order for the ball not to miss the crack, the minimal width of the crack (delta x) should be the expression in the red box in the pic.

http://img43.imageshack.us/img43/6563/scan0001fon.jpg [Broken]

How can I find the connection between (delta v) and v?

Thanks.

## The Attempt at a Solution

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The uncertainty principle states in brief that when you measure momentum and distance you relate the two in the form

delta_p * delta_x >= h/2 where h is Plancks constant and the deltas are the statistical deviations from the mean of the random variable.

If you want a good mechanism on explaining quantum mechanics you should read a book by Feynman and Hibbs called the Path Integral formulation written by a famous physicist called Richard Feynmann. It goes into great detail explaining the formulation of quantum mechanics using functionals.

I'm about to study it myself in great detail but I have seen a copy already and it is very very good.

Basically the derivation involves assuming a gaussian distributed random variable and then taking the various deviations on that variable. There is a better explanation of this in books involving descriptions of wave mechanics.

Anyway hope that helps.

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asi123 said:

## Homework Statement

Hey guys.

I have this kid throwing a ball with mass M and from high H.
He is trying to hit a crack in the floor.
I need to show that in order for the ball not to miss the crack, the minimal width of the crack (delta x) should be the expression in the red box in the pic.

http://img43.imageshack.us/img43/6563/scan0001fon.jpg [Broken]

How can I find the connection between (delta v) and v?

Thanks.
Kind of a weird problem... you'd think that in order for the ball not to miss the crack, the ball has to be smaller than the crack! :tongue: I have a suspicion that this is not a proper application of the uncertainty principle. But I probably shouldn't say anything without knowing how to solve the problem, and right now I can't see any connection between the physical situation and the answer you're supposed to get.

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## 1. What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental concept in quantum mechanics that states that it is impossible to know both the position and momentum of a particle with absolute certainty.

## 2. How does the Uncertainty Principle relate to the Minimal Width of Crack?

In the context of the Minimal Width of Crack, the Uncertainty Principle states that it is impossible to know both the position and velocity of a crack with absolute certainty. This is because measuring the position of the crack would disturb its momentum, and vice versa.

## 3. What is the significance of the Minimal Width of Crack in materials science?

The Minimal Width of Crack is an important concept in materials science as it helps us understand the behavior of cracks in materials. It allows us to make predictions about the crack's growth and propagation, as well as the strength and durability of materials.

## 4. How is the Minimal Width of Crack calculated?

The Minimal Width of Crack is calculated using the Uncertainty Principle formula, which states that the product of the uncertainty in position and momentum is always greater than or equal to a constant value, known as Planck's constant.

## 5. Can the Minimal Width of Crack be measured accurately?

Due to the Uncertainty Principle, it is impossible to measure the Minimal Width of Crack with absolute accuracy. However, scientists have developed techniques to estimate the minimal width and make predictions about the behavior of cracks in materials.