Wave-like Properties of a Cadillac Passing Through a Freeway Underpass

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SUMMARY

The discussion revolves around calculating the speed and time required for a Cadillac, with a mass of 2000 kg, to achieve a wavelength that allows for diffraction when passing through a 10m wide freeway underpass. The de Broglie wavelength formula, λ = h/p (where p is momentum), is utilized to derive the necessary speed of 3.3 x 10^-38 m/s. Additionally, the time taken to traverse the 10m distance at this speed is calculated to be 9.6 x 10^30 years, highlighting the impracticality of the scenario compared to normal freeway speeds of 30 m/s.

PREREQUISITES
  • Understanding of de Broglie wavelength and its application in physics
  • Knowledge of momentum and its calculation (p = mv)
  • Familiarity with basic kinematics, particularly distance, speed, and time relationships
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the de Broglie wavelength concept in quantum mechanics
  • Learn about momentum and its implications in classical and quantum physics
  • Explore kinematic equations and their applications in real-world scenarios
  • Investigate the principles of wave-particle duality in physics
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Students of physics, particularly those studying quantum mechanics, as well as educators and anyone interested in the wave-like properties of matter and their implications in real-world scenarios.

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Homework Statement



A Cadillac with a mass of 2000kg approaches a freeway underpass that is 10m across. at what speed must the car be moving, and how long would it take to go the 10m, in order for it to have a wavelength such that it might somehow diffract after passing through this single "slit"? How do these conditions compare to normal freeway speeds of 30m/s?

Homework Equations



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The Attempt at a Solution



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well, I have no idea how to solve this question...
first of all, I cannot imagine what's going on here, partly because I'm not a native english speaker...

Can someone teach me the way to solve this, in detail?
the answers are 3.3*10^-38 m/s and 9.6*10^30 yr.
 
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I really don't see the point of this exercise - but they want you to use the de Broglie wavelength=h/p (where p is the momentum). Just set wavelength roughly equal to the 'slit' size of 10m and figure out v. Then figure out how long it would take you to cross 10m at that velocity.
 
ah-huh, i kind of understood the question now.
Thank you!
 

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