PHYSICS-1
BALLISTIC PENDULUM
EXPERIMENT 8 – Ballistic Pendulum
OBJECTIVE
The purpose of this experiment is to measure the initial velocity of a projectile in two
independent ways: One by treating it as a projectile moving according to the kinematic
equations, and the other is by applying the conservation of linear momentum and energy to a
ballistic pendulum.
MATERIALS
Ballistic Pendulum
Meter stick
Carbon paper
Triple beam balance
White paper
INTRODUCTION
If the projectile is fired horizontally with an initial velocity Vo, it will follow the parabolic path
shown in figure 1.The horizontal range X and vertical displacement Y of the projectile are given
by:
X = Vo T
(1)
Y = (1/2) g T 2
(2)
Combining the above equations allows to determine Vo , given by equation ( 3 )
(3)
The initial velocity Vo of the projectile can also be determined by using the ballistic pendulum
(Fig 2). It consists of a spring gun that fires a metallic ball of mass m which is caught by a catcher
at the end of a pendulum of mass M. The collision between the ball and pendulum is perfectly
inelastic. As a result, the combination swings upward until it stops at the highest point by a
ratchet.
From conservation of momentum,
mVo = ( m + M ) V1
(4)
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PHYSICS-1
BALLISTIC PENDULUM
where V1 is the common velocity of pendulum – ball just
after collision. If the combination rises through a height h,
then from conservation of mechanical energy we have:
(1/2) ( m + M ) V12 = ( m + M ) g h
(5)
By combining ( 4 ) and ( 5 ) we determine the velocity Vo
to be:
Vo =
(m+M)
m
√(2gh)
(6)
Therefore, we can find the speed Vo of the projectile in two
different ways and compare our results.
EXPERIMENTAL PROCEDURE
Part 1 Projectile Motion
1) Move the pendulum out of the path of the ball, and secure the ballistic pendulum to the
table.
2) Place the ball in the shaft in the un-cocked position and measure the height Y from the
bottom of the ball to the ground by using a plumb line.
3) Fire the gun few times to get an approximate position of where it strikes the ground, and
then tape a piece of white paper and center it around where the ball lands. You can cover it
with a carbon paper if you wish.
4) Shoot the ball at least five times and record the horizontal positions of each mark left on the
paper.
Part 2
Ballistic pendulum
5) Remove the pendulum from the apparatus and measure its mass M and that of the ball m.
6) Reinstall the pendulum and record the distance between the base of the apparatus and the
center of mass ( CM ) of the pendulum; (this is the location of the pin protruding from the
pendulum).
7) Place the ball in the shaft and cock the gun until the shaft is locked in position. Fire the gun
and after the ball comes to rest on the curved rack, record the vertical distance between the
base of the apparatus and the center of mass of the pendulum. Repeat this procedure five
times and record your results.
ADDITIONAL INFORMATION
http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html
http://hyperphysics.phy-astr.gsu.edu/hbase/class/phscilab/balpen.html
http://www.youtube.com/watch?v=dny7AvR5Gfc
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PHYSICS-1
BALLISTIC PENDULUM
EXPERIMENT 8 – Ballistic Pendulum
REPORT FORM
Name ___________________________________________
Part 1
Date ______________
Projectile Motion
Shots
Range, X
Deviation from the average
1
2
3
4
5
Average
Vertical distance Y __________
Velocity Vo of projectile from ( 3 ) _____________
Part 2
Ballistic Pendulum
Mass ‘M’ of pendulum _________
Mass ‘m’ of ball
_________
Trials
1
2
3
Height of CM at its
lowest point
Height of CM at its
highest point
Vertical distance h
Velocity Vo of projectile from ( 6 ) _____________
Percent difference between the two values of Vo
3
_____________
4
5
Average
PHYSICS-1
BALLISTIC PENDULUM
CALCULATIONS
1)
Calculate the average value for the range X of the projectile as well as its average
deviation.
2)
Using equation ( 3 ), calculate the initial velocity V o of the projectile.
3)
Calculate the average value for the vertical distance h the pendulum-ball system has risen
after the collision. This is the difference between the height of CM at its highest point and
that at its lowest point.
4)
Using equation ( 6 ), calculate the initial velocity V o of the projectile.
5)
Calculate the percent difference between the two values of Vo (i.e. by eqn. 3and eqn. 6)
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PHYSICS-1
BALLISTIC PENDULUM
EXPERIMENT 8 – Ballistic Pendulum
Post- Laboratory Questions
Name: __________________________________________
1)
Using your experimental results, calculate the fractional loss in kinetic energy during the
collision.
2)
Prove, by making use of equation ( 1 ), that this fractional loss is equal to:
3)
To what has this loss of energy been converted into?
4)
Derive Equation ( 6 ).
5)
Explain why it would have been incorrect to equate the initial kinetic energy of the ball to
the final potential energy of the system.
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