Transcript THE BALLISTIC PENDULUM Students: Pedro N. Placido, Jr. Aziz Kenz. Ryan Ramnarine. SC 441H Spring 2002, Dr.

THE BALLISTIC
PENDULUM
Students:
Pedro N. Placido, Jr.
Aziz Kenz.
Ryan Ramnarine.
SC 441H Spring 2002, Dr. Roman Kezerashvili
OBJECTIVES:
1.
2.
3.
Study one-dimensional Inelastic
Collision between two objects.
Determine the Linear
Momentum.
Verify the principals of
conservation of Mechanical
Energy and Linear Momentum for
Ballistic Pendulum Experiment .
Theory:
Formulas:
1
2
Ei  (m  M )V  (m  M ) gy1
2
E f  ( m  M ) gy2
Ei  E f
m v  ( m  M )V
Formulas:
(Velocity)
V 
2 g ( y 2  y1 ) 
mM
v
m
2 gh
mM
2 g ( y 2  y1 ) 
m
d  vt
2 gh
Formulas:
(Kinetic energies)
2
mv
Ki 
2
2
( m  M )V
Kf 
2
Kf
m

Ki
mM
Data:
Table #1:
Determination of the initial velocity of the ball with the ballistic
pendulum.
Mass of
ball m,
kg.
Mass of
pendulu
m M, Kg.
Distance
y1, m.
Distance
y2, m.
Height
h = y2–y1
Velocity
of BallPendulu
m M,
m/s2.
Initial
velocity
of ball v,
m/s.
.07
.266
.072
.161
.809
1.321
6.34
Table #2:
Determination of the velocity of the ball from Distance-Time
measurements.
Distance between
photogates, m.
Average time t, s.
Average velocity of
ball, m/s.
.08
(.013 + .012) / 2 =
.0125
(6.154 + 6.667) / 2 =
6.41
Table #3:
Determination of the fractional loss of kinetic energy.
Kinetic
energy before
collision Ki , J.
Kinetic
energy after
the collision
Kf , J.
Fractional
loss
1-( Kf / Ki )
Fractional
loss
1-( m / (m +
M))
Percent
difference of
the ratios.
1.41
0.2932
0.7921
0.7917
.05%
Computations:
mM
v
2 gh
m
(0.07  0.266) Kg
v
0.07Kg
v  6.332m / s
V 
2 gh
V 
29.810.089
V  1.321m / s
2(9.81)(0.089) m 2 / s 2
m v2
K i
2
0.07(6.332) 2
Ki 
 1.4 J
2
Kf

m  M V 2

2
2

0.07  0.2661.321 Kgm2 / s 2
Kf 
2
K f  0.29J
Kf
0.29J
1
 1
 0.99
Ki
1.4 J
Kf
m

, then
Ki m  M
Kf
m
1
 1
 0.79J
Ki
mM
1
K f  ( m  M )V
2
1
K i  m v2
2
so,
Kf
Ki
Kf
Ki
Kf
Ki
Kf
Ki
( m  m)V

m v2

2
(m  M )

 (m  M ) 
m

m




m (m  M )
2

2
mm  M 
m

mM
2
2 gh
2


2
2 gh

2 gh 
2 gh
2
2

2
Conclusion:
We conclude that both Linear Momentum
and Mechanical Energy are conserved in
Ballistic Pendulum Experiment. These
concepts are also an important source to
understand inelastic collisions.
THE BALLISTIC
PENDULUM
Thank You, to all
our class mates,
and to Dr. Roman
Kezerashvili.