Physics of the Sweet Spot on a Baseball Bat

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The focus of my research is isolating and locating the
"sweet spot" on a baseball bat. I chose to avoid presenting
raw data, but to examine the science that causes
this reaction. Participants of this sport probably
have first hand or an intuitive knowledge of this saying. Locating the
"sweet spot" can be done at home. A simple experiment
of your on can be done using either a wood or aluminum
bat. The only apparatus required is a hammer. Gripping the bat
by the handle suspend perpendicular from the floor. Using a hammer, tap
in various places on the barrel of the bat. As you approach the
center of the barrel, vibration from the force will diminish.
Vibrational modes will be detected from the hand gripping the bat.

Every baseball bat has a “sweet spot.” When a baseball hits a bat in the wrong place your hands “sting,”
it means the force of the collision has excited waves or vibrations called modes. When the ball is hit at
the node it will not sting your hands. A mode generates two nodes or a position of zero displacement.
A baseball bat consists of two major nodes; this region is proverbially known as the “sweet zone.” Higher
frequency modes affect the ball speed, but can hardly be felt by the batter. Baseball bat vary in lengths,
but generally the “sweet spot” is approximately 17 cm from the end of the barrel of a major league baseball bat.

A collision near the node reduces the vibrations felt by the hand. The existence of the
“sweet spot” is mainly because the vibrations do not agitate at that particular node. Impact on the first
node will not excite the first mode, but will affect the second mode. Thus is true for the second node’s
relationship with the first mode.

Close to where the point of percussion occurs is the “sweet spot.” According to a
study done by H. Brody at the Physics Department of the University of
Pennsylvania, “A bat of mass M and with initial velocity zero can be treated
as a free-body that is hit by a ball whose momentum changes due to
the interaction.” At the time of percussion the bat will oscillate which indicates
a transferal of kinetic energy into vibrational energy and some kinetic energy is lost.
When all this occurs it is an extremely aggressive action. The bat has a
massive force on the ball changing the direction and speed.


Newtons Second Law of Motion
"An unbalanced force causes an object to move in the direction of the force.

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"Physics of the Sweet Spot on a Baseball Bat." 17 Dec 2017
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Net Force (F)
F=ma is equal to mass times acceleration

Conservation of linear momentum
Total Momentum (p)
when the net force acting on a system of a object is zero,
the total momentum (p) of a system is constant.

Elastic Collision
A collision between two objects where no kinetic energy
is lost and energy is conserved.

Conservation of energy
Energy can neither be created nor destroyed, it can only change from forms.
The total energy of an isolated system is constant regardless of internal changes

Note: A net force hit on a small mass will go farther than a large mass.


R. Cross, “The sweet spot of a baseball bat,” American Journal of Physics. 66, 772-779 (1998).

H. Brody, “Models of baseball bats,” American Journal of Physics. 58, 756-758 (1998).

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