Solving Uncertainty Principle Problem with Car and Toll Gate

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Homework Help Overview

The problem involves a car approaching a toll gate, with specific dimensions and constraints regarding its speed and clearance. It touches on concepts from physics, particularly the Heisenberg uncertainty principle and possibly de Broglie wavelength, as participants explore the relationship between speed, dimensions, and uncertainty.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to relate the problem to the Heisenberg uncertainty principle but expresses confusion about its application to the scenario. Other participants question whether the problem is a trick question and suggest it might be solvable without invoking the uncertainty principle. There is also a mention of a similar problem involving electrons, raising questions about the relationship between uncertainty and wavelength.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the potential irrelevance of the uncertainty principle, and there is an acknowledgment of differing perspectives on the nature of uncertainty in this context.

Contextual Notes

Participants are grappling with the application of quantum mechanics concepts to a classical mechanics problem, and there is uncertainty about the definitions and relationships involved in the problem setup.

tempest33k
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I am having trouble getting going on this problem and I'm hoping someone can help get me started.
A car with a mass of 1000 kg approaches a toll plaza. The clearance on either side of the car as it passes through the toll gate is 1 m. (a) What is the minimum speed at which the car can approach the gate and be reasonably sure of not scraping on either side? (b) How many years will it take the car to go through the gate if it is 5 m long?

I have no idea how to do solve this. Originally I thought about using Heisenberg's uncertainty principle and setting delta x = 1 m. Yet I don't see how the uncertainty in that direction is related to a perpendicular velocity that the car would be approaching in. Perhaps I just don't understand the concept fully, as I don't see why there is a minimum speed I must be going to be sure I won't hit the side.

I will be grateful for any help.
Cheers.
 
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Is it possible this is a trick question? Sounds to me like it can be solved without invoking HUP.
 
I have a similar problem to tempst33k's .. this time with electrons. It seems the wavelength (uncertainty?) is in the direction of travel and my interest is in the 'size' normal to the direction of travel.

A comment on whether the 'uncertainty' and wavelength are or are not the same would be most appreciated.

Can anyone help please?
 
I don't like these types of problems.

Sounds like de Broglie.

Regards,
George
 

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