PASCO ME-6815 PROJECTILE CATCHER ACCESSORY - Manual (Page 10)

Projectile Catcher Accessory 012-05091E
6
To find the muzzle velocity of the ball,
we begin with the potential energy of the
pendulum at the top of its swing and
work backwards from there. From our
equation for energy conservation (2):
(3) v = 2gh
Substitute (3) into the equation for
momentum conservation (1):
m
b
v
o
= m
b
+ m
c
2gh
v
o
=
m
b
+ m
c
m
b
2gh
For comparison, the initial speed (muzzle velocity) of the ball is determined by shooting
the ball horizontally off the table onto the floor and measuring the vertical and horizontal
distances through which the ball travels.
For a ball shot horizontally off a table with an initial speed, v
0
, the horizontal distance ("x")
traveled by the ball is given by x = v
0
t, where t is the time the ball is in the air. Air friction
is assumed to be negligible.
The vertical distance the ball drops in time t is given by y = 1
2
gt 2 .
The initial velocity of the ball can be determined by measuring x and y. The time of flight
of the ball can be found using
t =
2y
g
and then the muzzle velocity can be found using v
o
= xt .
Part I: Determining the Initial Velocity of the Ball
Set Up
1. Clamp the Projectile Launcher to a sturdy table (near one end of the table).
2. Adjust the angle of the Projectile Launcher to zero degrees so the ball will be shot off
horizontally, away from the table onto the floor.
Procedure
1. Put the steel ball into the Projectile Launcher and cock it to the long range position. Fire
one shot to locate where the ball hits the floor. At this position, tape a piece of white paper
to the floor. Place a piece of carbon paper (carbon-side down) on top of this paper and tape
it down. When the ball hits the floor, it will leave a mark on the white paper.
2. Fire about ten shots.
Figure 1.2: Conservation of Energy
v h
v = o