®
M o d e l N o . M E - 9 8 9 2
E x p e r i m e n t 1 : B a l l i s t i c P e n d u l u m
9
012-09842C
Analysis
1.
Use your value of
max
, the distance
r
, and Equation 1.5 to calculate the maxi-
mum height (
h
) that the center of mass rises as the pendulum swings up (see Fig-
ure 1.3).
(eq. 1.5)
h
=
r
(1 - cos (
max
))
h
= _____________________
2.
Use your value of
h
and Equation 1.4 to calculate the launch velocity of the ball.
V
0
= _____________________
Question
The theory for this experiment ignores the rotational inertia of the pendulum. Because
the pendulum is not really a simple pendulum (a point mass on a massless rod), a sys-
tematic error is introduced. Does this simplistic analysis tend to give a launch velocity
that is too high or too low? (See Experiment 3 for a more exact treatment.)
Further Study
Use two photogates to measure the launch velocity of the ball. Compare this value to
the value you found using the ballistic pendulum.
x
h
r
q
max
x
=
r
cos (
max
)
r
=
x
+
h
Figure 1.3:
Calculating
h