Experiment 7
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 V o
, 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 = V o
T
Y = (1/2) g T
2
Taking the value of T from (1) and substituting in (2) we get equation (3) as
V
0
= X [g /2Y]
1/2
(1)
(2)
(3)
The initial velocity V o 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. This ball 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 (m + M) swings upward until it stops at the highest point by a ratchet.
From conservation of momentum, mV o
= ( m + M ) V
1
( 4 ) where V
1 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 ) V
1
2
= ( m + M ) g h
By combining ( 4 ) and ( 5 ) we determine the velocity V o
to be:
( 5 )
V
0
= [(m + M) / m][2g / h]
1/2
( 6 )
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Experiment 7
Therefore, we can find the speed V o
of the projectile in two different ways, equ.(3) and equ.(6) and compare our results.
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 uncocked 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.
REPORT FORM
Part 1 Projectile Motion
Shots
1
2
3
4
5
Average
Range, X Deviation
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Experiment 7
Vertical distance Y __________
Velocity V o
of projectile from ( 3 ) _____________
Part 2 Ballistic pendulum
Mass M of pendulum _________
Mass m of ball _________
1 Trials
Height of CM at its lowest point
2 3 4 5 Averages
Height of CM at its highest point
Vertical distance h
Velocity V o
of projectile from ( 6 ) _____________
Percent difference between the two values of V o _____________
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 V o
.
Review Questions and Exercises
Due before lab begins. Answer in the space provided.
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.
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Experiment 7
5) Define a perfectly inelastic collision. Give two examples of such a collision.
Post- laboratory Questions and Exercises
Due after completing lab. Answer in the space provided.
1) Using the value for V o calculated from the ballistic pendulum, calculate the fractional loss in the kinetic energy during the collision.
2) To what has this loss of energy been converted into?
3) Derive Equation ( 6 ).
4) 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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