So You Want to Hit a Home Run?

Karlene Joseph                  Walther Lutheran High School
                                900 Chicago Avenue
                                Melrose Park IL 60160
                                708-344-0404

Objectives:

1.  Students will demonstrate a relationship between the position of the 
baseball bat and the baseball at the point of contact to direct the ball in the 
appropriate hitting field.
2.  Students will determine the center of percussion and the center of mass for 
a baseball bat.
3.  Students will analyze the projectile motion of the path taken by a baseball 
as it is thrown in the air as well as the projectile motion of the path taken by 
a tossed bat that is made to flip over itself while in flight. 
4.  Students will find the center of mass for several irregularly shaped 
objects and relate this concept to the playing of sports in general.

Materials needed:

Per Lab Group:                                  
Baseball bat, meterstick, string, push pin, two transparencies, weighted object, 
tape (masking or colored), Baseball (or substitute tennis ball for safety 
purposes), flat board slightly larger than the width of a baseball bat, flat 
irregularly shaped object (cut from styrofoam, manila folders, or any material 
that is relatively stiff) 

Per Class:
Video camera, blank video tape
Video tape of portions of a baseball game
VCR with slow motion or frame by frame motion

Strategy:

Begin lesson with a video of portions of a baseball game that involve pitching, 
strike outs, fly balls to each field, bunts, home runs, line drives, and foul 
tipped balls.  Ask students to watch for physical factors that are involved in 
the playing of the game of baseball.  Make a list of these observations on the 
chalkboard.  Encourage a discussion of how physics is related to baseball.  
The focus of the lesson will be on batting.
Investigation #1    Ball and Bat Contact
Use a flat board instead of a bat for this portion.  (A flat board is used to 
concentrate on the angle of the bat and to eliminate human errors and skills 
that influence what is observed.)  Students toss the ball at the board while 
the board is held at different angles.  Students record their observation of how 
the ball rebounds off the board in a data table that includes these types of 
hits:  infield fly, fly ball to each field, ground ball, line drive, foul ball-
left or right, foul tipped ball almost straight up.  Drawing diagrams of the 
angles and paths may be helpful in the data chart. 
Investigation #2    Get to Know Your Bat
Hold the bat gently from the handle so that the bat hangs downward.  Tap the 
ball all along the edge of the bat from top to bottom.  (There is one spot on 
the bat that sounds and feels more solid.)  Mark this spot with tape. 
Investigation #3    The Sweet Spot 
Hold the bat horizontally and firmly from the handle.  Drop the ball from a 
height of about 10 cm above the bat so that the ball hits the bat and bounces 
off.  Do this for about 5 to 10 different places on the bat, making sure to 
include the spot that was taped in investigation number 2.  Graph the height the 
ball bounces vs. the position on the bat. (The ball bounces highest at the 
marked spot. The marked spot is called the sweet spot by baseball players and 
the center of percussion by scientists.)  To illustrate the center of percussion 
and its importance to the baseball player suspend a meterstick by a string from 
a small hole drilled in one end.  For a uniform meterstick, the center of mass 
should be at the 50 cm mark and the center of percussion should be roughly 20 cm 
below the center.  Hit the meterstick at various locations to try to cause the 
meterstick to swing.  (At the center of percussion, the meterstick swings in a 
wide arc with very little rotation about the vertical axis.  At other points on 
the meterstick, the meterstick wobbles, twists, and vibrates quite a bit more. 
If the ball contacts the bat at the sweet spot most of the energy from the bat 
is transferred to the ball in the forward direction since energy is not lost due 
to rotational motion.  The batter's hands sting less since the bat was not 
caused to vibrate.)
Investigation #4    Balance Your Bat
Balance the bat horizontally on one finger.  Mark this spot with a piece of 
contrasting tape.  (This place is the center of gravity for the object.  For 
most objects this place is also the center of mass.) 
Investigation #5    Toss Your Bat and Ball
In front of a video camera, toss the ball in the air so that it travels in an  
arc for a horizontal distance of about 5 meters.  Still in front of the video 
camera, toss the bat so that it flips over itself as it travels, in an arc again 
about 5 meters horizontally.  Students should describe in as much detail as 
possible the two motions observed.  (A good taping of the motion is important 
here.  Choose a uniform background that will provide contrast.  Do not move the 
camera with the motion, instead focus on a central point of the background.  It 
may take some practice to make sure the entire path is recorded in the space  
allowed.) 
Investigation #6    Analysis of the Paths of the Tossed Bat and Ball
Tape a transparency to the TV screen.  Play the tape the students made in slow 
motion or frame by frame.  Students plot on the transparency the piece of tape 
that marks the center of mass for the bat as they see its position on the TV 
screen.  Do the same for the position of the ball as it crosses the screen.  
(Both paths plotted should be the typical parabolic shape of a projectile.  This 
could be done as a class with a few students helping with the plotting, however 
it is better to allow each group to plot their own segment.  Investigations #7 
and #8 may be done during this time by other groups who are not working with the 
VCR.  The centers of mass for any object will follow a parabolic shape 
regardless of the motion of other parts of the object.) 
Investigation #7    The Center of Mass for Irregularly Shaped Objects
Using string and push pins, suspend the irregularly shaped object from a point 
near the edge.  A weighted string hangs from the point of suspension.  Students 
draw the line formed by the string on the object. Several points of suspension 
are chosen.  (The vertical line passing through the point of support must also 
pass through the center of gravity.  Since the center of gravity and the center 
of mass are at the same location, the intersection of several of the points will 
determine the center of mass.) 
Investigation #8     People Have Centers of Mass, Too
Stand against a wall so that the heels, legs, and back are all touching the 
wall.  Try to touch your toes so that the heels and legs are still touching the 
wall.  (As the student leans forward the majority of his/her center of gravity 
is no longer over his/her feet, therefore the student will fall before touching 
the toes.) 

Performance Assessment:

1.  Give students a few shapes, both regularly shaped and irregularly shaped.  
Have a dot somewhere within the shape, some shapes may have the dot at the 
center of mass while others should not.  Tell students that the dot represents 
the center of mass for the shapes.  Ask the students the following questions:
Do you agree or disagree with the placement of the dot to represent the center 
of mass?  Why or why not?  What might you do to prove yourself correct in each 
case?  Why would your method work?
2.  Make or buy a ball that has an off-centered weight in it.  (The "GUAC" ball)
Toss a ball, and the weighted ball in the air.  Ask students to observe the two 
motions.  Are the paths what you would expect?  Explain and justify your answer. 
3.  Sometimes when hitting a baseball, a batter's hands will sting.  What is 
causing the sting?  Why is the sting not present every time the batter contacts 
the ball? 

Scoring Rubric:
5 points:  Answers correctly with clear, sound, multi-faceted, logical arguments 
(diagrams, examples, sketches, etc.)
4 points:  Answers correctly with clear explanation
3 points:  Answers correctly but reasons unclearly
2 points:  Partially correct with effort toward explanations
1 point:   Answers with no supporting evidence
0 points:  Answers of "I don't know"

Conclusions:

Center of gravity is an important concept used in sports, not just baseball.  A 
player cannot balance if the center of gravity is not over or under the support 
base.  In sports in which flips and turns of the body are important, such as 
diving and gymnastics, the athlete's center of mass will still follow a 
parabolic path while the other portions of the athlete's body will be rotating 
around this center.  An extension of this lesson could be the assignment of 
individual reports on the origin of several sports that involve projectiles or 
centers of mass, such as the javelin throw, shot put, discuss, basketball, 
baseball, darts, diving, gymnastics, golf, archery, the trapeze, juggling, and 
so forth. 

Evaluations:

Discussion of results and discoveries after each investigation seems to be a 
better method than group discussion at the end of all activities.