Question

Let’s assume that the speed of a typical racing car can be recorded to an accuracy of 0.001 kph.
Assuming the track distance is known to an accuracy of 0.01 km, is the uncertainty principle
violated for a 1-tonne car? Why or why not?

Answer 1

No, it's not. Strictly speaking, in terms of position and momentum, the uncertainty principle says:\[\Delta x \Delta p \ge \frac{ ħ }{ 2 }\]
Given that substitute your values:
\[\Delta x = 0.01km = 10m\]\[\Delta p = 1 tonne*0.001kph = 1000kg *0.00028m/s = 0.28kg∙m/s\]\[\Delta x \Delta p = 10m*0.28kg∙m/s = 2.8kg∙m ^{2}/s\]\[\frac{ ℏ }{ 2 } = 1.055*10^{-34}kg∙m ^{2}/s\]So, you end up with an uncertainty 2*10^34 times greater than the Uncertainty Principle requires. All is well with Heisenberg. This case points out that generally violations of the Uncertainty Principle are not a concern in the macro world.

Answer 2

thanks, it's really helpful