Question

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 the 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?

Answer 1

The percent uncertainty in the distance is 0.0593%, the uncertainty in the elapsed time is 1 second, the average speed is 391 m/s, and the uncertainty in the average speed is 0.231 m/s.

Step-by-step explanation:

1. To calculate the percent uncertainty in the distance, we divide the uncertainty in distance by the measured distance and then multiply by 100%. In this case, the percent uncertainty is (25 m / 42188 m) × 100% = 0.0593%.
2. The uncertainty in the elapsed time is simply the given uncertainty of 1 second.
3. To calculate the average speed, we divide the measured distance by the measured time. The average speed is 42188 m / (2 h + (30 min × 60 s/min) + 12 s) = 391 m/s.
4. The uncertainty in the average speed can be calculated by taking the product of the percent uncertainties in distance and time. The uncertainty in the average speed is (0.0593% + 0%) × 391 m/s = 0.231 m/s.

Answer 2

speed of golf ball is 1.15 ×
`10^(-30)` m/s

and % of uncertainty in speed = 2.07 ×
`10^(-30)` %

Step-by-step 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 ≥
`(h)/(4\pi )` ......1

Δx × ΔPx ≥
`(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 =
`(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)` %