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Ballistic Pendulum
Lab #4
xxxxxx
Physics 11
11/13/06
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View Full Document Introduction/Purpose
The purpose of this lab is to find the initial velocity of a ball shot from a springloaded
gun. For Investigation 1, a ballistic pendulum will be used along with concepts of energy
and momentum. Since the ball will be shot into the pendulum and immediately caught,
the collision will be perfectly inelastic. This means that momentum is conserved during
the collision
V
m
M
mv
)
(
0
+
=
where
V
is the velocity of the ball and pendulum immediately after the collision. Now
that the velocity of the pendulum and ball is known, it is possible to establish a statement
that relates the energy at the bottom to the energy at the pendulum’s highest point. Since
the total energy is conserved, the potential plus kinetic energy should be the same at the
bottom and the top. If the height of the pendulum at its lowest point is said to be zero, it
will have only kinetic energy at the bottom and only gravitational potential energy at the
top
gh
m
M
V
m
M
)
(
)
(
2
1
2
+
=
+
where
h
is the distance in the
y
direction that the center of mass moves through. Solving
for
V
and then plugging in to the momentum equations yields
gh
m
m
M
v
gh
V
2
2
0
+
=
=
Now in Investigation 2, the initial velocity of the ball shot from the springloaded gun
will again be found. This time, however, concepts of projectile motion will be utilized.
One way to find the initial velocity of the ball is to use the equation for range
t
R
v
=
0
The range,
R
, can be determined by measuring the distance in the
x
direction that the ball
flew. This still leaves the time of flight unaccounted for. Time is related to the height that
the ball started. Since there was no initial velocity in the
y
direction, the following
equations describe the time of the flight
g
y
t
gt
y
2
2
1
2
=
=
where
y
is the height of the center of mass of the ball above the table. Plugging this value
of
t
into the range equation should give the initial velocity of the ball. The ultimate goal
of the lab is to show how two separate methods can be used to find the same quantity,
velocity.
Experiment/Data
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This lab report was uploaded on 03/31/2008 for the course PHYSICS 11 taught by Professor Rogertobin during the Fall '06 term at Tufts.
 Fall '06
 RogerTobin
 Physics

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