Question

Calculate the uncertainty in the position of the soccer ball kicked by Rafael Marquez during the 2018 World Cup qualifying match between Mexico and US prior to score the second goal for Mexico. Assume the soccer ball has a mass 230 grams and it was traveling at 150 kilometers per hour and the velocity is known down to 0.1 kilometers per hour. Assume there is no uncertainty in the mass.

Answer 1

The uncertainity can be given as,

The uncertainty can be given as, Delta x times Delta v greaterthanorequalto h/4 pi where m is the mass and delta v is the uncertainty in velocity. Now, we have to substitute the values. Delta x times 0.23 kg times 0.1 times 277778m greaterthanorequalto h/4pi be cautions of the units Delta x greaterthanorequalto h/4pi times 0.23 kg times 0.1 times 0.277778 m/s Delta x greaterthanorequalto 8.253 times 10^33m

Where delta x is the uncertainity in position, delta p is the uncertainity in momemtum and h is the Planck constant.

Momentum can be written as,

$\Delta x*m\Delta v\geq \frac{h}{4\pi }$

where, m is the mass and delta v is the uncertainity in velocity.

Now, we have to substitute the values.

$\Delta x*0.230kg*0.1*0.277778m/s\geq \frac{h}{4\pi }$

(be cautious of the units)

$\Delta x\geq \frac{h}{4\pi *0.230kg*0.1*0.277778m/s}$

$\Delta x\geq 8.253*10^{-33}m$