Calculate the uncertainty in the velocity of a wagon of mass 2000 kg w

1.	Calculate the uncertainty in the velocity of a wagon of mass 2000 kg whose position is known to an accuracy of \(\pm\)10 m.
Answer» Mass of wagon = 2000 kg Uncertainty in position, ∆x = \(\pm\)10 m According to Heisenberg uncertainty principle ∆x × ∆p = \(\frac{h}{4\pi}\) ∆x × m∆v = \(\frac{h}{4\pi}\) or ∆x × ∆v = \(\frac{h}{4\pi m}\) ∆v = \(\frac{h}{4\pi m\Delta \mathrm{x}}\) = \(\frac{6.626\times10^{-34}kgm^2s^{-1}}{4\times3.14\times(2000kg)\times(10m)}\) = 2.636 × 10⁻³⁹ ms⁻¹

Calculate the uncertainty in the velocity of a wagon of mass 2000 kg whose position is known to an accuracy of \(\pm\)10 m.

Answer»

Mass of wagon = 2000 kg

Uncertainty in position, ∆x = \(\pm\)10 m

According to Heisenberg uncertainty principle

∆x × ∆p = \(\frac{h}{4\pi}\)

∆x × m∆v = \(\frac{h}{4\pi}\)

or ∆x × ∆v = \(\frac{h}{4\pi m}\)

∆v = \(\frac{h}{4\pi m\Delta \mathrm{x}}\)

= \(\frac{6.626\times10^{-34}kgm^2s^{-1}}{4\times3.14\times(2000kg)\times(10m)}\)

= 2.636 × 10⁻³⁹ ms⁻¹