User's Manual

®
Model No. ME-6830 Exp. 5: Conservation of Energy
012-05375C 27
Exp. 5: Conservation of Energy
Equipment Needed
*Use the Photogates and Photogate Mounting Bracket with a PASCO Interface or Timer to measure the initial speed of the ball
directly (see Experiment 2).
Purpose
The purpose of this experiment is to confirm that the initial kinetic energy of a
projectile shot straight up is transformed into an equal amount of gravitational
potential energy.
Theory
The total mechanical energy of a projectile is the sum of its gravitational poten-
tial energy and its kinetic energy. In the absence of friction, total mechanical
energy is conserved. When a projectile is shot straight up, the initial gravitational
potential energy (GPE) can be defined as zero. The initial kinetic energy (KE)
depends on the mass, m, of the projectile and the initial speed, v
0
:
When the projectile reaches its maximum height, h, the speed of the projectile is
zero and therefore the kinetic energy is zero. The gravitational potential energy
depends on the mass of the projectile and the height:
where g is the acceleration due to gravity. If friction in the form of air resistance is ignored, the initial kinetic
energy should equal the final gravitational potential energy.
The initial speed of the projectile must be determined in order to calculate the initial kinetic energy. To calculate
the initial speed, v
0
, of a projectile fired horizontally, the horizontal distance travelled by the projectile is x = v
0
t
where t is the time that the projectile is in the air.
The vertical distance that projectile drops in
time, t, is given by
The initial speed of the projectile can be calcu-
lated by measuring x and y and using y to calcu-
late the time, t. The time of flight of the
projectile can be found using
and then the initial speed can be found using
Item Item
Projectile Launcher and plastic ball Plumb bob and string
Meter stick or measuring tape Sticky tape
White paper Carbon paper
Photogate Head ME-9498A (2) optional* Photogate Mounting Bracket ME-6821A optional*
CAUTION!
DO NOT LOOK
DOWN BARREL!
CAUTION!
DO NOT LOOK
DOWN BARREL!
CAUTION!
DO NOT LOOK
DOWN THE BARREL.
LONG
RANGE
MEDIUM
RANGE
SHORT
RANGE
Position
of Ball
Launch
SHORT RANGE
PROJECTILE LAUNCHER
ME-6800
Yellow Band in Window Indicates Range.
90
8
0
7
0
6
0
5
0
40
3
0
20
10
0
WEAR SAFETY GLASSES WHEN IN USE.
Use 25 mm
balls ONL Y!
Figure 5.1: Conservation
of Energy
final
position
initial
position
h
v
0
KE
1
2
---
mv
0
2
=
GPE mgh=
y
x
υ
0
Figure 5.2: Find the initial speed
y
1
2
---
gt
2
=
t
2y
g
------=
v
0
x
t
--
=