PASCO ME-6831 Ballistic Pendulum_Projectile Launcher - Manual (Page 43)

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M o d e l N o . M E - 6 8 3 0 E x p . 9 : P r o j e c t i l e V e l o c i t y — E x a c t M e t h o d
0 1 2 - 0 5 3 7 5 C 39
Exp. 9: Projectile Velocity—Exact Method
Equipment Needed
Purpose
The muzzle velocity of the projectile launcher is determined by launching the ball into the ballistic pendulum and
observing the angle to which the pendulum swings.
As derived earlier in the manual, the equation for the velocity of the ball is approximately:
where M is the mass of the pendulum and ball combined, m is the mass of the ball, g is the acceleration due to
gravity, R
cm
is the distance from the pivot point to the center of mass of the pendulum, R
p
is the distance from the
pivot point to the ball,
 is the angle reached by the pendulum, and I is the moment of inertia of the pendulum with
the ball in the catcher.
The value of I can be found by measuring the period of small oscillations of the pendulum/ball combination and by
using the equation:
where T is the period.
Setup
1. Put the Projectile Launcher on the Ballistic Pendulum upright at the level of the ball catcher (the low posi-
tion). Make sure that the pendulum can hang vertically without touching the launcher.
2. Clamp the Ballistic Pendulum base to a sturdy table. Make sure that the clamp does not interfere with the pen-
dulum swing.
Procedure
1. Latch the pendulum at 90° so it is out of the way temporarily, and then load the projectile launcher with the
steel ball. Allow the pendulum to hang freely, and move the angle indicator to zero degrees.
2. Fire the launcher and record the angle reached. If you want to do the experiment with a lower or higher angle,
add to or remove mass from the pendulum. Repeat these test measurements until you are satisfied with the
mass of the pendulum.
3. Once you have chosen the mass to use for your experiments, remove the pendulum from the upright by
unscrewing and removing the axle. Use a mass balance to find the mass of the pendulum and ball together.
Record this value as M in Table 9.1.
4. Measure the mass of the ball alone and record this as m.
Item Item
Ballistic Pendulum/Projectile Launcher and steel ball Ruler
C-clamp Mass balance
String Stopwatch
v
b
1
mR
b
---------- 2IMgR
cm
1

cos –
 
=
I
MgR
cm
T
2
4
 2
------------------------ =