Question

B) A baseball of mass 0.15 kg thrown at 100 mph has a momentum of 6.7 kg x m/s. if the uncertainty in measuring this momentum is 1.0 x 10^-7 of the momentum, calculate the uncertainty in the baseballs position.

Answer 1

Answer B -

Mass of Baseball = 0.15 kg

Speed = 100 mph or 44.704 m/s [1 mph = 0.44704 m/s]

momentum = 6.7 kg.ms^-1

uncertainty in measuring momentum = 1.0 * 10^-7

uncertainty in position = ?

We know that,

$\Delta$p * $\Delta$ x = h/4$\pi$ ----------------------A

where, $\Delta$ p = uncertainty in momentum

$\Delta$x = uncertainty in position

h = plank's constant (6.62607004 × 10^-34 m² kg / s)

$\pi$ = 3.14

Also,

$\Delta$p = uncertainity in measurement * p

$\Delta$p = 1.0 * 10^-7 * 6.7 kg.ms^-1

$\Delta$p = 6.7 * 10^-7 kg.ms^-1

Now put all the values in A

$\Delta$p * $\Delta$ x = h/4$\pi$

6.7 * 10^-7 kg.ms^-1 * $\Delta$ x = 6.62607004 × 10^-34 m² kg/s / 4 * 3.14

$\Delta$x = 6.62607004 × 10^-34 m² kg/s / (4 * 3.14 * 6.7 * 10^-7 kg.ms^-1)

$\Delta$x = 7.87 * 10^-29 m [Answer]