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LAB# 14
PROJECTILE MOTION AND THE CONSERVATION OF ENERGY
Figure 1: Equipment for the "Projectile Motion and Conservation of Energy" experiment
showing the projectile launcher, projectiles, loading rod, photocells (photogates) and safety
glasses.
INTRODUCTION:
Our objective in this experiment is to analyze projectile motion using
kinematics and also using conservation of mechanical energy.
Analyzing a system from
different viewpoints often allows one to gain additional insight into the system, as well as into
the methods used.
We begin by using the kinematical relationships for a projectile moving with
constant acceleration (the acceleration due to gravity here) to determine the initial speed (muzzle
velocity) of a projectile fired horizontally.
We than use this initial speed to predict the horizontal
range of the same projectile fired at some angle to the horizon.
We will also measure the initial
speed of our projectile using photocells.
We end by applying conservation of mechanical energy
to our projectile to determine if initial kinetic energy and maximum gravitational potential
energy are equal for a projectile fired straight up into the air.
APPARATUS:
Projectile launcher and kit, Plumb bob; a meter stick and a 2-meter stick;
Carbon paper; White paper; C-clamp; LabPro Interface;
Lab# 14 Projectile Motion
program, safety glasses.

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Theory:
Using the coordinate system shown in Figure 2 we have for the
x
and
y
positions of the projectile
as a function of time,
,
0
t
v
x
x
(1)
.
2
2
1
0
0
gt
t
v
h
y
y
(2)
Where
v
x0
and
v
y0
are the
x
and
y
components of the projectile’s initial velocity
v
0
.
h
0
is the
projectile’s initial height above the origin and
g
is the acceleration due to gravity.
Note that
the negative sign in front of
g
comes from our choice of up as the positive
y
direction.
The
independence of the x and y components of the motion tell us that the time it takes the
projectile to reach the ground is independent of the horizontal motion.
That is, it does not
matter how fast or slow the projectile is traveling horizontally. The time it takes the
projectile to reach the ground depends only on the projectile’s initial height, its initial speed
in the vertical direction, v
y0
, and of course g.
Given that, if we wish to measure the
projectile’s initial speed,
0
v
, we fire the projectile horizontally,
0
0
v
v
x
, measuring the
distance
x
Total
it travels horizontally before it hits the ground,
.
0
t
x
v
Total
(3)
The time t is the time it takes an object to fall to the ground, y = 0, from an initial height of
h
0
is,
.
2
0
g
h
t
(4)
Direct measurement of
x
Total
along with combining Equations (3) and (4), left as an exercise
for you, will yield the initial speed of the projectile.

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