Experiment 5: rackets, bats and "sweet spots – PASCO ME-6950 PAScar with Mass User Manual

Page 16

012-07361B

PAScar with Mass

Experiment 5: Rackets, Bats and "Sweet Spots"

EQUIPMENT NEEDED:

– PAScar (ME-6950)

– Metric tape (SE-8712)

– Meter stick or a long rod

Purpose

When a batter or tennis player strikes a ball, a portion of the rotational kinetic energy of
the bat or racket is transferred to the ball. In a somewhat oversimplified picture, the
motion of the bat or racket can be thought of as a simple rotation about a pivot which is
located near its end and close to the batter’s wrists. The portion of the bat’s original
kinetic energy that is transferred to the ball depends on the distance y between the point
of impact and the pivot point. The position on the bat corresponding to the maximum
energy transfer is called a “sweet-spot." We will call this maximum energy sweet-spot
SS1.

NOTE: For simplicity, it is assumed
that the collisions are perfectly elastic.

Theory

As any batter can tell you, if you hit
the ball at a certain point on the bat,
there will be no shock, or impulse,
transferred to your hands! This
“sweet-spot” is generally located at a
different position than SS1 and is
called the “percussion point." We
will call this zero-impulse sweet-spot
SS2. For a given “bat” and pivot, the
position of SS2 can be found from:

where I is the rotational inertia of the bat for the corresponding pivot, m is the total mass
of the bat, and y

is the distance from the pivot to the center of mass of the bat. (e.g. If a

uniform rod of length L is pivoted about an end-point, SS2 is located at 0.67L from the
pivot.)

The positions of both SS1 and SS2 can be found theoretically, or by using the Sweet-Spot
computer program (see page 18 for details). The position of SS2 can be found experi-
mentally using the PASCO Force Sensor or, roughly, by actually hitting a ball at a variety
of positions on the bat and noting where the least shock to your wrists occurs. In this
experiment, a method for determining the location of SS1 is described.

Using a meter stick or rod as a bat (see Figure 5.1), the PAScar can play the role of a ball.
By observing how far the car rolls after impact, the relative, or even absolute energy
transfer can be determined for various values of y. In this manner, SS1 can be found.

Figure 5.1

NOTE: Release the

stick from the same

position each trial.

Pivot point

(EQN-1):

SS2