GateWay CC
INITIAL
OF ROJECTILE MOTION
VELOCITY
PHY101 Physics Lab:
Purpose
The purpose of this lab is to find the initial velocity of a projectile motion using ballistic
pendulum. Initial velocity of an object will be calculated using two methods:
a) Using the principle of conservation of momentum and
conservation of energy during the collision
Theory
There are two methods to calculate the initial velocity of the object in trajectory motion –
velocity of the projectile.
Measurement of velocity using ballistic pendulum is based on the principle of
conservation of momentum and conservation of energy. The gun is fired into pendulum
bob, which then swings in an arc trajectory. A mechanism – catcher, catches the bob at
its heights point of swing. If m is the mass of the bob and M is the mass of the catcher,
based on the principle of conservation of momentum:
m  vi  (m  M )  v f
where:
vi - is the initial velocity of the of the bob just before the collision.
vf - is the final velocity of the bob and catcher joined after the collision.
m  vi - momentum of the system before the collision. This momentum is the momentum
of just the bon. Catcher is at rest before the collision so its momentum is equal to zero.
(m  M )  v f - momentum of the system after the collision. This is the momentum of bob
and catcher joined together.
Bob with mass m
Bob with mass m
vf
vi
Catcher with mass M
Catcher with mass M
Just before the collision
Just after the collision
If we solve last equation for initial velocity of the bob:
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vi 
mM
vf
m
In order to find initial velocity vi we also need to calculate final velocity vf.
Right after the collision bob and catcher together have a kinetic energy:
KE 
1
(m  M )  v 2f
2
This energy is converted into potential energy at the final point of swing of bob and
catcher:
PE  (m  M )  g  h
where:
g – gravitational acceleration and
h – is the vertical rise of bob and catcher during the swing.
Base on the principle of conservation of energy:
KE  PE
1
(m  M )  v 2f  (m  M )  g  h
2
From the last equation we can find the final velocity – velocity just after the collision.
vf  2 g h
Let’s now substitute vf into equation of vi:
vi 
mM
mM
vf 
 2 g h
m
m
INITIAL SETUP
1.
2.
3.
4.
Ballistic pendulum consists on a base-trigger assembly, a pendulum post assembly, and
three one-inch balls, two steel and one aluminum ball.
Attach the pendulum post assembly to the base by fitting the two guiding pins at the
bottom of the post assembly into the holes in the top of the base and threading the knob
through the bottom of the base and into the post. Make sure that the post assembly is
tightly fastened to avoid inconsistent results.
Position the assembled ballistic pendulum at the edge of a lab bench and level the base
of a pendulum.
4. Adjustment of the sphere velocity can be made by turning the sleeve on the horizontal
shaft which is located on the end of the trigger assembly furthest from the pendulum
post assembly. Rotation of the sleeve changes the tension on the spring inside the trigger
assembly and produces a noticeable effect only after several complete turns. It is easier
to turn the adjustment sleeve before the trigger assembly is in the "cocked" position. The
adjustment sleeve should not be changed until both parts of the experiment are
completed.
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Ballistic pendulum
Procedure
The mass m of the sphere should be determined on a balance. (The steel sphere has an
approximate mass of 66 g). The effective mass of the catcher (116 g) appears on the rear of the
trigger housing assembly since the catcher cannot be removed and measured separately, The
center of the mass of the catcher/sphere appears as a red dot on the catcher. The difference
between the height of this dot before and after the sphere is projected into the catcher is the
increase in height h in the equations above. To use the ballistic pendulum most effectively,
proceed as follows:
1. Be sure that the assembly instructions at the beginning of this description have been
followed carefully.
2. To fire the sphere, slide the sphere onto the horizontal rod projecting toward the
pendulum post assembly and its catcher. Be sure the sphere is firmly seated. The firing
mechanism is armed when the sphere and rod are pushed horizontally away from the
catcher until the trigger engages
3. After the mechanism is armed, loosen the knob on top of the post so that the pendulum
can swing freely. Push the alignment pin (the small rod with red plastic ends) to the rear.
Do not let the pendulum and sphere strike the horizontal rod when resetting as this may
deform the rod end.
4. IMPORTANT: If consistently accurate readings are to be made, the next instruction must
be followed exactly. With the top knob loose, guide the pendulum until it touches the
sphere. Hold it there while tightening the knob on the top of the post. After the knob is
tightened. Before letting the pendulum go, bring the alignment pin to the front. Then let
the pendulum swing gently back until it touches the alignment pin. At that point, gently
pull the pin to the rear. This operation exactly aligns the pendulum in the vertical position
and reduces backlash in the roller clutch.
5. Measure the vertical distance h1 from the base to the red dot on the catcher.
6. Fire the pendulum by tapping down on the trigger lever located directly above the
sphere. The sphere will be propelled forward to hit the pendulum catcher, becoming
trapped in the rubber wedges and causing the pendulum to fly upwards. The roller clutch
will stop the pendulum at the peak of its flight and prevent it from dropping back down to
its starting position.
7. Determine the vertical distance h2 from the base to the red dot on the catcher.
The difference between this distance and that measured in step 5 is the height h
= h2 - h1.
8. Repeat steps 2 through 7 about ten times and at the end calculate the average
values. After measuring, loosen the knob and let the pendulum slowly return to
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GateWay CC
the starting position. CAUTION: Do not let the sphere and catcher strike the
horizontal red. To do so may cause deformation of the rod.
9. From the equations given above, find the initial velocity of the sphere just before
it hits the catcher. This is a value determined by assuming that momentum is
conserved during the collision and mechanical energy is conserved after the
collision.
Data Table and Data Analysis
Object – Aluminum sphere
Nr.
m
kg
M
kg
h2
m
h1
m
h
m
vi
m/s
M
kg
h2
m
h1
m
h
m
vi
m/s
1
2
3
4
5
6
7
8
9
10
Avr
Object – Steel sphere
Nr.
m
kg
1
2
3
4
5
6
7
8
9
10
Avr
Analysis/Questions
1. What are the probable reasons for the difference between the values of the projectile
velocity obtained by the two methods?
2. Using the average values determine the energy of the projectile before and after the
collision between the sphere and the catcher. Are these two energies the same, and why?
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