Friday, November 23, 2012

Andy Pettitte’s Fastball

By Kate Allaway

Andy Pettitte has pitched for the Yankees for a total of 12 years and in that time has been an all-star 3 times and has won numerous awards. He is also major league baseball’s all time wins leader in the post season with 19 post season wins. Pettitte throws a four-seam fastball, a cutter, a curveball, a sinker, a changeup, and a slider.

Here I will look at his fastball and determine the force it exerts on a baseball bat.

His fastballs typically have a speed of 91 mph, or 41.7 m/s.
Vo = 0 m/s
Vf = 41.7 m/s
Distance from pitcher’s mound to home plate = 18.39 m
Vf 2= vo2 + 2a(Δx)
(41.7 m/s)2 = (0 m/s)2 + 2a(18.39 m)
a = 47.3 m/s2

mbaseball= 145g = 0.145 kg
Fexerted by baseball=(0.145kg)(47.3 m/s2)=6.9 N

Would this force break a (stationary) bat?

Ultimate (shear) strength of the wood of a bat=5x106 N/m2
Estimate that about a circle with a radius of 1 cm (A= 3x10-4 m2) of the ball comes in contact with the bat

Stress = (6.9 N/3x10-4 m2) = 23,000 N/m2

Thus, Pettitte’s fastball would not break a bat that is unmoving. However, if one took into consideration the movement of the bat, the bat’s construction (with thinner and thicker points) and the distance of the ball’s force from the moving bat’s axis of rotation, we could see why bats do sometimes break.

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