EXPERIMENT 9 – 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 kinematics 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)
:
1
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)
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:
(6)
Therefore, we can find the speed Vo of the projectile in two different ways and compare our
results.
Also from here V1 = √2gh
( Note: V1 is the velocity of the pendulum with the ball embedded in it.
(7)
We can now calculate Vo by using Vo = { m+M/m}V1
(8)
2
EXPERIMENTAL PROCEDURE
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.
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.
3
EXPERIMENT 9 – Ballistic Pendulum
REPORT FORM
Name ______________________
Professor _____________________
Date _____________________
Part 1
Projectile Motion
Shots
1
2
3
4
5
Average
Range, X
Deviation
Vertical distance Y __________
Velocity Vo of projectile from ( 3 ) _____________
Part 2
Ballistic pendulum
Mass M of pendulum _________
Mass m of ball
_________
Trials
Height of CM at its
lowest point
1
2
3
Height of CM at its
highest point
4
4
5
Averages
Vertical distance h
Velocity Vo of projectile from ( 6 ) _____________
Percent difference between the two values of Vo
_____________
CALCULATION
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 Vo 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 Vo of the projectile.
5) Calculate the percent difference between the two values of Vo .
5
EXPERIMENT 9 – Ballistic Pendulum
Review Questions and Exercises
Name _____________________
Due before lab begins. Answer in the space provided.
Date ___________________
1) Derive equation ( 3 ) and show that the path of the projectile is parabolic.
2) If the speed of a particle is doubled, by what factor is its momentum changed?
By what factor is its kinetic energy changed?
3) One person is standing perfectly still, and then takes a step forward.
Is linear momentum conserved? Explain.
4) A bullet of mass 12 grams is fired into a large block of mass 1.5 kg suspended from light vertical
wires. The bullet imbeds in the block and the whole system rises 10 cm. Find the velocity of the
bullet just before collision.
5) Define a perfectly inelastic collision. Give two examples of such a collision.
6
EXPERIMENT 9 – Ballistic Pendulum
Post- laboratory Questions and Exercises
Name __________________
Due after completing lab. Answer in the space provided.
Date _____________________
1) Using the value for Vo calculated from the ballistic pendulum, calculate the fractional loss
in the 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.
7
8