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posledela
3 years ago
13

Consider a golf ball with a mass of 45.9 grams traveling at 200 km/hr. If an experiment is designed to measure the position of t

he golf ball at some instant of time with a precision of 1 mm, then what will be the uncertainty in the speed of the golf ball? What percentage of the speed of the golf ball does this uncertainty represent?
Physics
1 answer:
Kipish [7]3 years ago
3 0

Answer:

speed of golf ball is 1.15 × 10^{-30} m/s

and % of uncertainty in speed =  2.07 × 10^{-30} %

Explanation:

given data

mass = 45.9 gram = 0.0459 kg

speed = 200 km/hr = 55.5 m/s

uncertainty position Δx = 1 mm = 10^{-3} m

to find out

speed of the golf ball and  % of speed of the golf ball

solution

we will apply here heisenberg uncertainty principle that is

uncertainty position ×uncertainty momentum ≥ \frac{h}{4\pi }    ......1

Δx × ΔPx  ≥ \frac{h}{4\pi }

here uncertainty momentum ΔPx = mΔVx

and uncertainty velocity = ΔVx

and h = 6.626 × 10^{-34} Js

so put here all these value in equation 1

10^{-3} × 0.0459 × ΔVx =  \frac{6.626*10^{-34}}{4\pi }

ΔVx = 1.15 × 10^{-30} m/s

and

so % of uncertainty in speed = ΔV / m

% of uncertainty in speed =  1.15 × 10^{-30}  / 55.5

% of uncertainty in speed =  2.07 × 10^{-30} %

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