Heisenberg Uncertainty Principle and Kinetic Energy

In summary, the minimum uncertainty in the position of the ball with a mass of 50 g moving at a speed of 30 m/s, measured to an accuracy of 0.1%, is 0.015 m. For the proton with a kinetic energy of 1.0 MeV, if its momentum is measured with an uncertainty of 5.0%, the minimum uncertainty in its position is 0.0058 m. This is based on the equation \Deltap\Deltax \geq\frac{h}{4\pi}.
  • #1
tatiana_eggs
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Homework Statement



18. A ball of mass 50 g moves with a speed of 30 m/s. If its
speed is measured to an accuracy of 0.1%, what is the
minimum uncertainty in its position?

19. A proton has a kinetic energy of 1.0 MeV. If its momentum
is measured with an uncertainty of 5.0%, what is
the minimum uncertainty in its position?


Homework Equations


[tex]\Delta[/tex]p[tex]\Delta[/tex]x [tex]\geq[/tex][tex]\frac{h}{4\pi}[/tex]


The Attempt at a Solution


I know how to solve #19, because I know that [tex]\Delta[/tex]p / p = uncertainty. But what about accuracy? Do they mean the same thing? How does accuracy relate to [tex]\Delta[/tex]p or [tex]\Delta[/tex]x or the uncertainty of one of those?

Thanks!
 
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  • #2
I believe they mean the same thing with accuracy.
 

What is the Heisenberg Uncertainty Principle and how does it relate to kinetic energy?

The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that states that it is impossible to know both the precise position and momentum of a particle at the same time. This uncertainty is directly related to the kinetic energy of the particle, as the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

How does the Heisenberg Uncertainty Principle affect our understanding of the physical world?

The Heisenberg Uncertainty Principle challenges our classical understanding of the physical world, which assumes that the properties of particles can be measured and known with absolute precision. It introduces an inherent uncertainty into our understanding of quantum systems and highlights the limitations of our ability to observe and measure the behavior of particles.

Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental law of quantum mechanics and has been extensively tested and confirmed through experiments. It is a fundamental limit to our ability to measure and understand the behavior of particles.

How does the Heisenberg Uncertainty Principle impact the development of new technologies?

The Heisenberg Uncertainty Principle has a significant impact on the development of technologies such as atomic clocks, electron microscopes, and quantum computers. These technologies rely on our ability to precisely measure the properties of particles, and the uncertainty principle sets a limit to this precision. It also guides the design and development of new technologies, as engineers and scientists must consider the uncertainty principle in their designs and calculations.

Is the Heisenberg Uncertainty Principle applicable to macroscopic objects?

In theory, the Heisenberg Uncertainty Principle applies to all particles, regardless of their size. However, the effects of uncertainty become negligible for macroscopic objects, as the uncertainty becomes smaller in comparison to the object's size and mass. The principle is most noticeable at the microscopic scale, such as with subatomic particles.

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