What is the Minimum Uncertainty in Block's Speed on a Frictionless Surface?

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Homework Help Overview

The problem involves a block resting on a frictionless surface, where the uncertainty in the block's position is given, and participants are tasked with determining the minimum uncertainty in the block's speed. The context relates to principles of quantum mechanics, specifically the Heisenberg uncertainty principle.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the Heisenberg uncertainty principle and how to correctly interpret the relationship between speed and velocity. There are attempts to calculate the uncertainty in speed based on the provided position uncertainty.

Discussion Status

Several participants have provided calculations and expressed differing results, indicating a lack of consensus on the correct approach or outcome. Some have pointed out potential sources of error in the calculations, while others are questioning the assumptions made regarding the definitions of speed and velocity.

Contextual Notes

Participants are working with a specific precision in measurement and are navigating the implications of using different interpretations of the uncertainty principle. There is mention of the potential for misunderstanding in the conversion between speed and velocity, which may affect the calculations.

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Homework Statement


A 1.70 kg block rests on the icy surface of a frozen pond, which you can assume to be frictionless. If the location of the block is measured to a precision of 0.30 cm, what is the minimum uncertainty in the block's speed, assuming the mass is known exactly?


Homework Equations


xp=h/4(3.14)


The Attempt at a Solution


xp=h/4(3.14)
x(mv)=h/4(3.14)
I plugged in all the values and got v. The answer was wrong. I then multiplies by .0003 and that was also wrong.
 
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potential sources of error # 1:
0.3 cm = 0.003 meters, not 0.0003 meters


potential source of error # 2
they ask you for uncertainty in speed, while the equation for momentum p = mu considers VELOCITY
an uncertainty in speed of 10m/s , for example, is equal to an uncertainty in velocity of 20 m/s, since a speed up to 10 m/s implies a range of velocities from -10m/s to +10m/s
so try multiplying the speed by 2 :) (edit: or rather, try dividing the uncertainty in velocity you get by 2 to get the uncertainty in speed, since the block moves in both directions)
 
1.03E-32 the velocity by 2 and got 5.16E-33 which is wrong by 10% to 100%.

I used .003 meters.
 
are you sure your math is right? using the version of the Heisenberg uncertainty principle that you've provided (there are many variations of it) and the values for m and deltax youve given,
i get an uncertainty in velocity of 3.24807255 × 10-32
which is an uncertainty in speed of 1.62403627 × 10-32
 
The math is right i did a million times. 1.62E-32 is wrong and it was last my chance. thanks, anways...
 

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