Physics is Fun! Baseball Teacher Guide

Episode Description
In Physics of Baseball Cheston and Jessica visit the McWane Center and the Physics of Sports exhibit. Through demonstrations, the assistance of Todd Jones and the Detroit Tigers, the teens explore the forces that come into play at home plate.
Curriculum Areas: Science/Math/Sports/Reading/Writing

Newton's Laws

• Law I (Law of Inertia)
An object at rest or in motion will continue at rest or in motion unless acted upon by a net external force. The more mass or inertia that an object has the more difficult it is to change its state of motion. If you were standing at the bottom of a hill, which would you rather try to stop from moving, a basketball or a runaway car? Which would be easier to hit off of a tee with a golf club - a golf ball or a bowling ball? How would you justify your answer?

• Law II
This law is best described by the popular equation, F = m X a. Unfortunately, this equation is misleading because it seems to suggest that acceleration can exist without a force or that force is dependent on acceleration. Written properly, the equation takes the form, a = F/m, stating the fact that acceleration is direct result of a net force. If there is no net force, there is no net acceleration. Thus, Newton's second law states that the acceleration of an object is directly proportional to the net force and inversely proportional to the mass. This law supports Law I in that for a given force, the more massive an object is, the less it will accelerate.

• Law III
For every action there is an equal and opposite reaction. Is it possible for one to touch without being touched or for a bat to hit a ball without the ball hitting the bat?

Bernoulli's Principle
Daniel Bernoulli, a Swiss scientist, discovered that the pressure of a gas or fluid, such as air, decreases as the velocity of the flow of that gas or liquid increases. This principle can be applied to many natural phenomena, ranging from explanations of how planes fly to why a baseball pitch curves.

Impulse and Momentum
N ewton's Laws state that force is equal to mass times acceleration, F = m x a, which is a measure of how much an objects linear momentum, p (mass x velocity), is changing over time (F = ?p / ?t). If there is no net external force, then linear momentum is not changing (?p = 0 Þ pfinal = pinitial) and, thus, it is said to be conserved. However, if there is a net external force (i.e. a bat hitting a baseball), there will be a resulting change in momentum either in direction, magnitude, or both. This is called impulse, I, which is related to the momentum and force by the equation

I = ?p = F ?t

Thus, the impulse is just the force being applied to an object multiplied by the time that the objects are in contact, which results in a change in momentum.

Preview Discussion
What can a pitcher do to keep a batter from hitting the ball?
What does a batter do to try to hit a home run?

Post Viewing Discussion
Discuss how the Concepts Covered relate to the Preview Questions.

Activities

Bernoulli's Principle
Materials Needed
Ping-Pong balls (2)
Tape, string or thread
Pencil
Piece of paper
A blow dryer (optional)
Water faucet with hot water.

Principles
Bernoulli's principle can be used to explain why a baseball curves. If we consider the flight of an airplane, the air moves across the top of the wings at a greater speed than it does underneath, due to the shape of the wings. As a result, the pressure on top of the wing decreases and is now lower than the pressure below the wings. It the difference in the two pressures is greater that the weight of the plane, the plane will lift and fly. A similar phenomenon occurs with a baseball that is spinning as it travels through the air. Because of the spinning motion, air resistance, and friction on the surface of the ball, the speed of airflow on one side of the ball will be much greater than the other side. Thus, the pressure will decrease on the side with greater airflow speed causing a pressure difference and movement of the baseball in the direction of least pressure.

Procedure #1
Tape string or thread of the same length to each Ping-Pong ball and attach to a pencil (or some other horizontal support). With the two Ping-Pong balls hung freely a few centimeters apart, use a blow dryer or your mouth to create airflow between the two balls. What do you observe? Where are the areas of lower and higher pressure?

Procedure #2
Fold a piece of paper in such a way that you make a "covered bridge". Place your folded piece of paper open side down on a flat surface. Again, using you mouth or a blow dryer, create an airflow that will go through the opening of your bridge. What do you observe? Once again, identify those areas of high and low pressures.

Extension
Critical Thinking. Suppose that you were to spin a Ping-Pong ball such that it is rotating in a counter-clockwise direction, as viewed from the top, and then you gently blow on the ball from the side. What did you think is going happen? Do you think the ball will move? If so, in what direction will the ball move and why? What if you spin the Ping-Pong ball, so that it is rotating in a clockwise direction, as viewed from the top?

Impulse and Momentum - Activity #1
Materials
Balloons
Eggs
Meter stick
Water
Plastic bags
Trash can.
Activity works best outside.

Principles
In baseball we often hear how important it is to have a "quick bat". But why is this so important? Also, why is it so much easier to hit a fastball out of the ballpark, as opposed to a curveball or changeup, which are slower pitches? The answer lies in the momentum or, more precisely, the change in momentum. When two objects collide or come into contact, Newton's laws mandate that they impart an equal and opposite force on each other resulting in a change in momentum either in direction, magnitude, or both. This change in momentum is called impulse, I, which is related to the momentum and force by the equation

I = ?p = F ?t.

The impulse is the force applied to an object multiplied by the time that the objects are in contact, which results in a change in momentum. Thus, for greater hitting power, we need to maximize our force or impulse by having a quick bat. A slower bat means less force during the time the ball and bat are in contact diminishing the impulse and the change in momentum. Alternatively, a faster pitch has more momentum, which translates to more force during the time of contact. Thus, we will have the same result.

Procedure
In groups of two, using an egg or a water balloon, toss the egg or balloon towards each other trying to catch them with you hands. After each successful toss, increase the separation between you and your partner by approximately a meter. Describe your approach to catching the egg or balloon on those successful attempts? When the balloon or egg finally broke, did you notice any difference in the way you tried to catch the balloon or egg and what was the difference?

For the Teacher
In this activity, by catching the egg or balloon we are attempting to bring the momentum of the egg or balloon to zero while not applying a force necessary to break either. Since the egg or balloon has a definite momentum, which can be assumed to be constant, successful attempts should be those in which the force is minimized and, as a result, the time of contact is maximized. Students who are most successful in this activity will tend to move their hands in the direction the egg or balloon is traveling as they attempt each catch minimizing the force during the time of contact, which is maximized. This explains how a catcher can catch 80 - 90 mile per hour fastballs without breaking his (or her) hands. However, instead of moving their hands in the direction the pitch is traveling, they are equipped with special catching mitts that have special padding that allows the time of contact to be increased and, thus, the force during that time is minimized. This is a common approach that students use in egg drop contests where some kind of padding is employed to soften or lessen the impact or impulse.

Impulse and Momentum - Activity #2
Math Extension

Materials Needed:
Basketball
Tennis ball
One or two meter sticks
Balance or scale
Stopwatch
Calculator

Principles
See impulse and momentum principles from previous section.

Objective
To calculate the approximate time of contact between two balls and the ground using concepts of force, impulse and momentum.

Procedures
1. Measure the mass of the basketball, MB, and the mass of the tennis ball, MT, in kilograms. (1 kg = 2.2. lbs.)
2. In student groups of three or four, practice dropping a basketball and tennis ball together (the tennis ball should be sitting on top of the basketball, as shown in the video) from a height of one meter.
3. Once you have mastered the drop, measure the time it takes for the balls to hit the ground after they are released. Record you results.
4. Now, repeat your drop(s) as you did in step #1. This time, however, measure how high the basketball and tennis ball bounce back up in the air, ?yB and ?yT, respectively. You may have to repeat several times for good results. As seen in the video, the heights of the two balls should not be the same. Hint: You may want to do this next to a wall that you can mark on or put tape on. Record you results.

Calculations
1. Since the acceleration (due to gravity) is constant during the time of fall, we can use kinematics equations to calculate the velocity or speed just before the balls hit the ground. The equation to use is

Vfy = voy - g t

where voy = 0 m/s, time, t, has been determined experimentally, and g " 10 m/s2. Record your result.
2. Using the height of each ball after the bounce, calculate the velocity or speed of each ball just after contact with the ground using the equation

Vf yB2 - VoB2 = -2 g ?yB
Vf yT2 - VoT2 = -2 g ?yT

where vfyB = vfyT = 0 for each ball, g " 10 m/s2, and ?y, which is positive, has been determined experimentally for each ball. Solve for VoB and VoT for each ball. (Note: Remember, velocities and ?y may have a negative sign, which indicate direction with up being positive. Speed may only be positive.)

3. Now calculate the change in momentum, ?p.
Impulse, I = ?p = [(MB ´ VoB) + (MT ´ VoT)] - [(MB + MT) ´ -Vfy] Record your result.

4. From Newton's 3rd Law, the force exerted on the balls by the ground will be equal and opposite to the force exerted on the ground by the balls. For simplicity's sake, we shall assume that this force, FG, is approximately constant and equal to the mass of the balls multiplied by the acceleration due to gravity, g.

FG = (MB + MT) ´ g

5. Use the following equation to calculate the time of contact between the balls and the ground, ?t.

Impulse, I = ?p = FG ´ ?t

Impulse, I = ?p = [(MB + MT) ´ g] ´ ?t

Solve for ?t.

Does your result seem reasonable? Explain.
How would you alter your experiment in order to decrease the impulse or change in momentum and the height that each ball bounces back in the air after hitting the ground?
What effect would your proposed change(s) have on the time of contact?
If you have time, repeat the experiment to test your hypothesis.

Curriculum Extensions

Reading/Writing: Read and write about a baseball personality
Write How-to Pitch (bat or catch) for an Elementary school student

Slide into These Resources:
Adair, Robert K. The Physics of Baseball

Exploratorium Science of Baseball
http://www.exploratorium.edu/baseball