WOLFRAM|DEMONSTRATIONS PROJECT

Average Force on a Batted Ball

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baseball's initial speed
v
0
(ft/s)
100
baseball's final speed
v
f
(ft/s)
100
average force on ball:
2040.0 lbs
release pitch
This Demonstration calculates the force exerted on a baseball by a swinging bat as a function of the initial speed of the pitched ball
v
0
and the final speed of the batted ball
v
f
. The change in momentum of the ball is equal to the impulse, which is the integral of the force
F(t)
over time:
t
f
∫
t
0
F(t)dt
. Thus the average force is
(p(
t
f
)-p(
t
0
))/(
t
f
-
t
0
)
, where the ball is in contact with the bat between times
t
0
and
t
f
, and
p=mv
is the momentum. High-speed photography shows that the time interval
t
f
-
t
0
is approximately 0.001 second. The weight of a regulation baseball is 5.25 ounces, or 5.25/16 pounds, which corresponds to a mass of
5.25/(16×32.2)=0.0102
slugs, using the Imperial system of units, with length in feet, time in seconds, mass in slugs, and force in pounds.
The average force is then given by
F=m(
v
f
-
v
0
)/(
t
f
-
t
0
)=0.0102(
v
f
-
v
0
)/0.001
.
The Demonstration also animates the collision of the pitched ball with the swinging bat.
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