PASCO ME-6814 Mini Catcher Accessory - Manual (Page 8)

Mini Catcher Accessory 012-06293A
4
The kinetic energy of the catcher (and ball) after the collision is converted completely to potential
energy at the top of the swing:
(2)
1
2
m
b
+ m
c
v 2 = m
b
+ m
c
gh
So 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)
Substitute (3) into the equation for momentum conservation (1):
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) travelled by
the ball is given by , where t is the time the ball is in the air. Air friction is assumed to be
negligible.
The vertical distance (y) the ball drops in time t is given by .
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
and then the muzzle velocity can be found using .
Part I: Determining the Initial Velocity of the Ball
Setup
➀
Clamp the Mini Launcher to a sturdy table near one end of the table. ( See Figure 1.3).
t =
2y
g
Figure 1.3. Setup for Part I: Determining V
0
, method 1
table
Mini Launcher
steel ball in flight
y
x
9 8 7 6 5 4 3 2 1 0 1 2 3 4
MINI LAUNCHER ME-6825
CAUTION
WEAR SAFETY GLASSES WHEN IN
DON’T PUSH PISTON WITH
v = 2gh
m
b
v
0
= m
b
+ m
c
2gh
v
0
=
m
b
+ m
c
m
b
2gh
x = v
0
t
1
2
gt 2
v
o
= xt
y=