User's Manual

®
Model No. ME-9845 Ballistic Pendulum Accessory
9
Calculations and Analysis
m = mass of catcher
m
o
=mass of car
v
o
=initial speed of car
V=speed of car and catcher immediately after collision (before swinging up)
h= change in height as car and catcher swing up
1. Using the measured height h, calculate the speed V of the car and catcher immediately after the
collision. During the swing (due to very little friction), one can assume that energy is conserved.
(m
o
+M)gh=½(m
o
+M)V
2
or
V=
During the collision, is energy conserved? Compare the kinetic energy before and after the
collision.
E
before
=½m
o
(v
o
)
2
E
after
=½(m
o
+M)V
2
Note that before the collision, only the car (m
o
) is moving (v
o
) and has kinetic energy. After the col-
lision, both (m
o
+M) are moving (V) and have kinetic energy.
Because this is a completely inelastic collision, you will find that a large percentage of the kinetic
energy disappeared. Calculate the energy ratio (E
after
/E
before)
. Where did the rest of the energy go?
Heat was generated in the collision.
If the experiment is repeated with a car with a different mass, how does the energy ratio
(E
after
/E
before)
change?
2. During the collision, is momentum conserved? Compare the momentum before and after the
collision.
(Momentum)
before
=m
o
(v
o
)
(Momentum)
after
=(m
o
+M)V
The momentums should be very similar, and in theory the same. However, you may not observe the
momentums to be exactly equal. In theory, energy is "lost" in an inelastic collision, but the
momentum of the system remains the same.
2gh