A baseball has a mass of 0.15 kg. If pitched at 40.0 m/s with a relative uncertainty of 1%, how uncertain is its position? A) 8.8 × 10⁻³⁴ m B) 1.1 × 10⁻³⁴ m C) 1.8 × 10⁻³³m D) 1.1 × 10⁻³²m

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Quizplus · Accepted Answer

The uncertainty in position can be calculated using the Heisenberg Uncertainty Principle, which states Δx * Δp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck's constant (approximately 1.05 × 10^-34 m^2 kg / s). Given the mass (m) of the baseball is 0.15 kg and its velocity (v) is 40.0 m/s with a 1% uncertainty, the uncertainty in momentum (Δp) can be calculated as 1% of the momentum (p = m*v), which is 0.15 kg * 40.0 m/s * 0.01 = 6.0 × 10^-2 kg m/s. Using the Heisenberg Uncertainty Principle, solving for Δx gives a value that matches closest to the option A, indicating a very small uncertainty in position, consistent with the principle's implications for macroscopic objects.

A Baseball Has a Mass of 0