Heisenberg Uncertainty Principle and Kinetic Energy

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SUMMARY

The discussion focuses on the application of the Heisenberg Uncertainty Principle in calculating the minimum uncertainty in position for a ball and a proton. For the ball with a mass of 50 g moving at 30 m/s and a speed measurement accuracy of 0.1%, the uncertainty in position can be derived using the formula \(\Delta p \Delta x \geq \frac{h}{4\pi}\). Additionally, for a proton with a kinetic energy of 1.0 MeV and a momentum uncertainty of 5.0%, the same principle applies to determine its position uncertainty. The relationship between accuracy and uncertainty is clarified, confirming they are synonymous in this context.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle
  • Knowledge of basic physics concepts such as mass, speed, and kinetic energy
  • Familiarity with momentum and its calculation
  • Ability to manipulate and interpret scientific equations
NEXT STEPS
  • Study the derivation of the Heisenberg Uncertainty Principle in quantum mechanics
  • Learn how to calculate momentum and kinetic energy for various particles
  • Explore the implications of measurement accuracy on uncertainty in physics experiments
  • Investigate real-world applications of the Heisenberg Uncertainty Principle in technology
USEFUL FOR

Students of physics, particularly those studying quantum mechanics, as well as educators and researchers interested in the principles of measurement and uncertainty in particle physics.

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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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I believe they mean the same thing with accuracy.
 

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