Question

For many years, hitters have claimed that some baseball pitchers have the ability to actually throw a rising fastball. Assuming that a top major leaguer pitcher can throw a 95-mph pitch and impart a 1800-rpm spin to the ball, is it possible for the ball to actually rise? Assume the baseball diameter is 2.9 in. and its weight is 5.25 oz.

Answer 1

Answer

given,

speed = 95 mph

N = 1800 rpm

diameter = 2.9 in

weight = 5.25 oz

$\omega = \dfrac{2\pi N}{60}$

$\omega = \dfrac{2\pi \times 1800}{60}$

   ω = 188.5 rad/s

U = 95 x 1.467 ft/s

U = 139.33 ft/s

calculate the ratio $\dfrac{\omega D}{2U}$

$\dfrac{\omega D}{2U}=\dfrac{188.5\times \dfrac{2.9}{12}}{2\times 139.33}$

    ratio = 0.163

coefficient of lift corresponding to 0.163 from the lift and drag coefficient

   C_L = 0.04

ρ is the density of air

Lift produce

  $L = \dfrac{1}{2}\rho U^2AC_L$

  $L = \dfrac{1}{2}\times 0.002389\times 133.33^2\times \dfrac{\pi}{4}\times D^2\times 0.04$

  $L = \dfrac{1}{2}\times 0.002389\times 133.33^2\times \dfrac{\pi}{4}\times (\dfrac{2.9}{12})^2\times 0.04$

     L = 0.04238 lb

weight

 $W = 5.25 oz \times 0.625 \times \dfrac{lb}{oz}$

     W = 0.32815 lb