PASCO ME-6831 Ballistic Pendulum_Projectile Launcher User Manual
Page 12
B a l l i s t i c P e n d u l u m / P r o j e c t i l e L a u n c h e r
B a l l i s t i c P e n d u l u m T h e o r y
®
8
012-05375C
The torque on the pendulum is thus:
For small angles,
, sin so if you make this substitution and solve for you get:
This angular equation is in the same form as the equation for linear simple harmonic motion:
So if you compare the two equations, linear and angular, you can see that the pendulum exhibits simple harmonic
motion, and that the square of the angular frequency (
2
) for this motion is:
Solving for I gives the desired result:
where T is the period of the pendulum.
•
NOTE: You used a small-angle approximation to find the equation for I, but I does not depend on
. This
means that you must measure the period T using small angle oscillations. Once you have calculated I with that
period, you may use that value of I regardless of the amplitude reached during other parts of the experiment.
Installing the Optional Photogate Bracket (ME-6821A)
The Photogate Bracket is an optional accessory for mounting one or two photogates on the Projectile Launcher to
measure the muzzle speed of the ball.
•
Prepare the Photogate Bracket by loosening the thumbscrew near the end of the bracket. Leave the square nut
in place on the end of the thumbscrew. Use the smaller (0.75 in) thumbscrews that are stored on the bottom
side of the bracket to mount one or two photogates to the bracket
•
Align the square nut of the bracket with
the T-shaped slot on the bottom of the
Launcher barrel and slide the nut into the
slot until the photogate nearest to the bar-
rel is as close to the muzzle as possible
without blocking the photogate beam.
Tighten the bracket thumbscrew to secure
the bracket in place.
I
R
cm
Mg
sin
–
=
MgR
cm
I
------------------
–
=
k
m
----x
–
2
x
–
=
=
2
MgR
cm
I
------------------
=
I
MgR
cm
2
------------------
MgR
cm
T
2
4
2
------------------------
=
=
Projectile
Launcher
barrel
Square
Nut
Thumb
screw
Photogate
Photogate
Photogate
Mounting
Bracket
T-slot
Thumb
screw
Install the Optional Photogate Bracket