Pasco Scientific ME-6825, Инструкция по эксплуатации и руководство по экспериментам

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012-05479A Mini Launcher
23
Experiment 5: Conservation of Energy
EQUIPMENT NEEDED
– Mini Launcher and steel ball – Plumb bob
– Measuring tape or meter stick – White paper
– (optional) 2 Photogates and Photogate Bracket – Carbon paper
– (optional) Timing System
Purpose
The purpose of this experiment is to show that the kinetic energy of
a ball shot straight up is transformed into potential energy.
Theory
The total mechanical energy of a ball is the sum of its potential
energy (PE) and its kinetic energy (KE). In the absence of friction,
total energy is conserved. When a ball is shot straight up, the initial
PE is defined to be zero and the KE = (1/2)mv
0
2
, where m is the
mass of the ball and v
0
is the muzzle speed of the ball. See Figure
5.1. When the ball reaches its maximum height, h, the final KE is
zero and the PE = mgh, where g is the acceleration due to gravity.
Conservation of energy gives that the initial KE is equal to the final
PE.
To calculate the kinetic energy, the initial velocity must be deter-
mined. To calculate the initial velocity, v
0
, for a ball shot horizon-
tally off a table, the horizontal distance travelled 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. See Figure 5.2.
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
and then the initial velocity can be found using v
0
= x/t.
Setup
➀
Clamp the Mini Launcher near one end of a
sturdy table with the Launcher aimed away from
the table. See Figure 5.1.
➁
Point the Launcher straight up and fire a test shot
on long range. Make sure the ball does not hit the
ceiling. If it does, use the medium range through-
out this experiment or put the Launcher closer to
the floor.
➂
Adjust the angle of the Mini Launcher to zero
degrees so the ball will be launched horizontally.
Figure 5.1: Conservation of Energy
90 80
70
60
50
40
30
20
10
0
10
20
30
40
MINI LAUNCHER
ME-6825
C
A
U
T
I
O
N
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W
EA
R
S
A
FE
TY
G
L
A
SS
E
S
W
H
E N
I N
U
S
E
.
D
O
N
' T
PU
S
H
P
I S
T
O
N
W
I T
H
F
I
N
G
E
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!
initial position
final position
v
0
h
Figure 5.2: Finding the Initial Velocity
x
v
0
t =
2 y
g