The Physics of Cheating in Baseball

Objective

The goal of this project is to determine whether "corked" baseball bats make the ball travel farther than unaltered wooden bats.

Introduction

When a batter hits a baseball, what determines how far the ball goes? If you think about it carefully, you can come up with quite a few variables, including:

• the speed of the bat,
• the weight of the bat (including how that weight is distributed),
• the angle of the swing,
• exactly where, along the length of the bat, the ball and bat make contact,
• exactly where, around the circumference of the bat, the ball and bat make contact,
• the speed and direction of the incoming pitch, and
• external factors such as wind, air pressure, and temperature.

This project concentrates on the first two variables: the speed of the bat and the weight of the bat.

When two objects collide, both the speed and the weight of the objects matter in determining the outcome. For example, think about marbles. The shooter marble is bigger and heavier than the regular marbles. When the heavier shooter marble collides with a lighter regular marble, the shooter knocks the regular marble a long way. If you do it the other way around, the regular marble doesn't knock the shooter very far because the regular marble weighs less. However, if you increase the speed of the regular marble, by shooting it harder, the increased speed tends to make up for the decrease in weight, and the faster-moving marble will knock the shooter farther.

This combination of speed and weight is called momentum in physics. Momentum is the product of the mass of an object and the velocity of the object. The variable for momentum is p, so the equation for momentum is:

p = m × v.

Going back to our batter, we can say that the more momentum the batter can create with the bat, the farther we would expect the ball to go when it is hit. To increase the momentum, a batter can use a heavier bat, and/or the batter can also try to swing the bat faster. As the weight of the bat is increased, at some point it becomes to heavy for the batter's muscles, and bat speed decreases. A lighter bat is easier to swing fast, but at what point does the decreased weight make more difference than the increased speed? In other words, what is the best balance between bat weight and bat speed?

You may have heard of baseball players "corking" their bats in order to try and hit the ball farther. A "corked" bat is one that has been drilled out at the end, with the hole filled up with cork or some other material, and then capped off so it looks like a regular bat. Because the filling material is less dense than the wood of the bat, "corking" makes the bat lighter. The end result is that the batter can swing the bat faster. But we've seen that decreasing the weight of the bat will decrease the momentum. Can the extra speed of the swing with a corked bat make up for the decrease in weight? That's what this project is designed to find out!

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• mass,
• velocity,
• momentum.

Questions

• What are two ways for a batter to increase the momentum of the bat?

Bibliography

• Here is a good introduction to the subject of corked bats:
  Wikipedia contributors, 2006. "Corked Bats," Wikipedia, The Free Encyclopedia [accessed November 6, 2006] http://en.wikipedia.org/w/index.php?title=Corked_bat&oldid=82050804.
• Here are a couple of interesting sites examining the science of baseball:
  • Staff, 2000. "The Science of Swat," Arizona Engineer Newsletter, College of Engineering and Mines, University of Arizona, Tucson [accessed November 6, 2006] http://www.engr.arizona.edu/newsletters/AEspring00/swat.html.
  • Exploratorium, 1998. "Science of Baseball," Exploratorium [accessed November 16, 2006] http://www.exploratorium.edu/baseball/index.html.
• This high-school level physics tutorial has excellent information on momentum and how to analyze collisions between objects:
  Henderson, T., 2004. "Momentum and Its Conservation," The Physics Classroom and Mathsoft Engineering & Education, Inc. [accessed November 8, 2006] http://www.physicsclassroom.com/Class/momentum/momtoc.html.
• Particularly for more advanced students, we recommend this book, especially Chapter 5, "Batting the Ball," and Chapter 6, "Properties of Bats":
  Adair, R.K., 2002. The Physics of Baseball, New York, NY: HarperCollins Publishers.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• 3 (or more) identical wooden baseball bats,
• drill with 1/2-inch bit,
• wood vise or clamping jig for holding bat securely,
• hammer,
• punch,
• filling material for bat, e.g.:
  • sawdust,
  • rubber balls,
  • cork sheeting;
• white glue,
• permanent marker,
• baseball,
• ball tee,
• tape measure,
• optional: spring-loaded device for swinging bat, which you design and build; suggested materials:
  • springs to provide power,
  • wood for anchor post, and bat support to hold bat at proper height for batting tee,
  • hinge to attach bat support to anchor post,
  • fasteners for putting the pieces together.

Experimental Procedure

Preparing the Bats

1. Safety Note: Have an adult drill the bats for you.
2. Set one bat aside and do not drill a hole in it. You will compare the performance of the "corked" bats to this unaltered bat.
3. Use the following procedure for preparing the "corked" bats:
   1. Clamp the bat securely in the wood vise.
   2. Mark the center of the wide end of the bat (not the handle end), and use the hammer and punch to dimple the wood so the drill bit won't slip when starting.
   3. Drill a 1/2-inch diameter hole no more than 6 inches deep, taking care to drill straight along the long axis of the bat. Pull back on the bit occasionally to clear sawdust from the hole.
   4. Fill the hole with the material to be tested (e.g., cork or sawdust or rubber balls). Pack the material tightly.
   5. Use a permanent marker to label the bat with the filling material used.
   6. Seal the end of the bat closed with a wood disk and glue (or sawdust and glue).
   7. Allow the glue to dry overnight before performing tests with the bats.

Testing the Bats

1. Now you need to test which bat can hit the ball the farthest. For each method that you try (see below), do at least 25 trials with each bat. Measure the distance that the ball travels from the tee until it first hits the ground. Calculate the average distance from all 25 trials. (More advanced students should also calculate the standard deviation.)
2. There are a couple of different methods you could use to perform the test:
   1. using an apparatus to simulate a swing with constant force, or
   2. swinging the bats yourself.
3. For the first method, you'll need to design and build a sturdy, spring-loaded device that can hold a bat horizontally at the height of the tee. When you pull back on the bat, you apply tension to the spring(s). When the tension is released, the bat swings forward, hitting the ball off the tee. By cocking the bat to the same angle each time, the force of the spring(s) is kept constant for each trial. The main support for the device needs to be firmly anchored to the ground. Exercise proper caution when using the device!
4. For the second method, you swing the bat yourself. Try the following:
   1. Do your best to swing the bats at the same speed, regardless of the weight of the bat. Based on what you learned about momentum when doing your background research, what do you expect the results will be? What actually happened? Were you surprised? Why or why not?
   2. Swing hard. Do you feel like you are swinging the lighter bats faster than the unaltered wooden bat? What do you expect the results will be this time? What actually happened? Were you surprised? Why or why not?

Variations

• Can you think of a way to measure your bat speed in order to calculate the momentum of the different bats when they hit the ball?
• Compare the peformance of aluminum vs. wooden bats of the same weight.
• Compare peformance of end-weighted vs. normally-weighted aluminum bats.
• There are other ways to alter the effective mass of the bat, all of them legal under Major League Baseball rules:
  • holding the bat further up the handle ("choking up") reduces the effective length of the bat,
  • cutting the end of the bat off to make it shorter,
  • turning down the diameter of the bat on a lathe.
  Design an experiment to investigate the effects of one or more of these methods on hitting distance

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