PASCO ME-6829 Mini Launcher Ballistic Pendulum - Manual (Page 9)

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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
9
Experiment 2: Ballistic Pendulum
Theory
The ballistic pendulum has historically been used to measure the launch velocity of a
high speed projectile. In this experiment, a projectile launcher fires a steel ball (of
mass m
ball
) at a launch velocity, V0 . The ball is caught by a pendulum of mass m
pend
.
As the momentum of the ball is transferred to the catcher-ball system, the pendulum
swings freely upwards, raising the center of mass of the system by a distance h.
The pendulum rod is hollow to keep its mass low, and most of the mass is concen-
trated at the end so that the entire system approximates a simple pendulum. During
the collision of the ball with the catcher, the total momentum of the system is con-
served. Thus the momentum of the ball just before the collision is equal to the
momentum of the ball-catcher system immediately after the collision:
(eq. 2.1)
where V is the speed of the catcher-ball system just after the collision, and
(eq. 2.2) M = m
ball
+ m
pend
During the collision, some of the ball's initial kinetic energy is converted into thermal
energy. But after the collision, as the pendulum swings freely upwards, we can
assume that energy is conserved and that all of the kinetic energy of the catcher-ball
system is converted into the increase in gravitational potential energy.
(eq. 2.3)
where g =9.81 m/s
2
, and the distance h is the vertical rise of the center of mass of the
pendulum-ball system.
Combining equations 2.1 through 2.3 (eliminating V) yields
(eq. 2.4)
Experiment Set-up
1. Attach the ballast mass to the bottom of the catcher.
2. Set up the equipment and software as described on pages 4–6
with the pendulum rod attached to the RMS at the end hole and
the catcher side of the pendulum facing the launcher. Do not put
the sliding counterweight on the pendulum rod.
Procedure
Record Data
1. Load the launcher and push the ball in to the third (fastest) posi-
tion.
2. Start data collection.
m
ball V0
MV =
1
2
---MV
2
Mgh =
V0 1
m
pend
m
ball
------------- +
⎝ ⎠
⎛ ⎞ 2gh
=
Catcher
side
Ballast
mass
Figure 2.1: Set-up