PASCO ME-9430 Dynamics Cart with Mass - Manual (Page 19)

012-04840E Dynamics Cart
15
®
y
x
Experiment 5: Rackets, Bats and "Sweet Spots"
EQUIPMENT NEEDED:
– Dynamics Cart (ME-9430) – Mass set (SE-8704)
– Metric tape (SE-8712) – Meter stick or a long rod
– Long horizontal table or board (3/4” x 1’ x 8’)
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 the 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 gener-
ally 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
cm
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 experimentally
using the PASCO Force Transducer 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 Dynamics Cart can play the role of a
ball. By observing how far the cart 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.
If you have already done the experiment to determine the coefficient of rolling friction for your
cart for the same surface that you will be using in this experiment, you can determine the
kinetic energy of the cart at the moment after impact since:
Figure 5.1
Pivot point
y
SS2
= (EQN-1)
I
my
cm
mv 2 = µmgx (EQN-2)
2
1