To what uncertainty (in m) can the position of a baseball traveling at 45.0 m/s be measured if the uncertainty of its speed is 0.10%? The ma

Question

To what uncertainty (in m) can the position of a baseball traveling at 45.0 m/s be measured if the uncertainty of its speed is 0.10%? The mass of a baseball is about 0.145 kg.

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Linh Đan 4 weeks 2021-08-18T03:48:56+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-18T03:50:28+00:00

    Answer:

    Δx ≥ 8 x 10^(-29) m

    Explanation:

    We will solve this using Heisenberg’s Uncertainty Principle which states that one cannot simultaneously measure with great precision both the momentum, and the position of a particle.

    Thus, mathematically, this is expressed as

    Δp ⋅ Δx ≥ h/4π

    where;

    Δp is the uncertainty in momentum;

    Δx is the uncertainty in position;

    h is Planck’s constant which has a value of 6.626 x 10^(−34) m²kg/s

    Furthermore, the uncertainty in momentum can be written as;

    Δp = m ⋅ Δv

    where Δv is the uncertainty in velocity while m is the mass of the particle.

    In this question, the mass of the baseball is 0.145kg or 145g with an uncertainty in velocity of 0.1%

    So, uncertainty in velocity = 0.1% x 45 = 0.045 m/s

    Thus, the uncertainty in momentum will be;

    Δp = 0.145kg x 0.045 m/s = 6.525 x 10^(-3) m.kg/s

    Now, let’s plug in the relevant data into the Uncertainty Principle equation and make Δx the subject.

    Thus;

    Δx ≥ (h/4π) x (1/Δp)

    Δx ≥ [(6.626 x 10^(−34))/(4π)] /(1/(6.525 x 10^(-3)))

    = 8.08 x 10^(-29) m

    If we round to one sig fig, the uncertainty in velocity, will be

    Δx ≥ 8 x 10^(-29) m

    0
    2021-08-18T03:50:39+00:00

    Answer:

    Using the heisenbergs uncertainty principle equation

    Δx . Δp \geq h / 4\pi

    first find the speed for 0.10% : 45 m/s / 100% = x / 0.10%

    ∴ Δv = 0.045 m/s

    Δx \geq 6.626×10^{-34}/ 4×\pi× 0.145×0.045

    Δx \geq 8.081×10^{-33}m

    Explanation:

    heisenbergs uncertainty principle equation allows to find the uncertainty position (in m) where one calculates the uncertainty speed of 0.10%  by simple  first identifying the uncertainty speed of 100%

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