PASCO ME-6829 Mini Launcher Ballistic Pendulum - Manual (Page 11)

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M o d e l N o . M E - 6 8 2 9 E x p e r i m e n t 2 : Ba l l i s t i c P e n d u l u m
11
Analysis
1. Use your value of θ
max
, the distance r, and Equation 2.5 to calculate the maxi-
mum height (h) that the center of mass rises as the pendulum swings up (see Fig-
ure 2.2).
(eq. 2.5) h = r (1 - cos (
θ
max
))
h = _____________________
2. Use your value of h and Equation 2.4 to calculate the launch velocity of the ball.
V0 = _____________________
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 ( θ
max
)
r = x + h
Figure 2.2:
Calculating h