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LAB #14 Projectile motion and the Conservation of Energy
Introduction:
This is a series of experiments that deal with the motion of objects and
conservation of total mechanical energy. The analysis will also allow us to predict where
a ball will land on the floor when it is shot off a table at some angle above the horizontal.
To do this, we must be able to measure the initial speed (muzzle velocity) of the ball.
Shooting the ball horizontally off of the table and measuring the vertical and horizontal
distances through which the ball travels, permitting the initial velocity to be calculated,
will measure muzzle velocity. The initial velocity so obtained will then be used to
calculate where the ball will land when the ball is shot at some angle.
Initial Horizontal velocity
can be measured as follows: For a ball shot horizontally off a
table with the initial speed v
x
=
!
0
t
0
the horizontal distance traveled by the ball before striking
the floor is given by
where t is the time that the ball is in the air. Air resistance is
disregarded. The vertical distance that the ball drops in time t is given as y = 1/2gt
2
.
Eliminating “t” from these equations permits the initial velocity of the ball to be shown
. For the time of flight use the equation for
vertical motion:
by measuring x and y. We obtain
v
0
=
gx
2
2
y
0
=
y
0
+
(
v
0
sin
)
t
"
(
1
2
)
gt
2
where y
0
is the initial height of the ball and the position of the ball when it hits the floor is
taken to be y = 0.
x
=
(
v
0
cos
)
t
Then use
to find the range by eliminating “t” from the two equations, and
solving the resulting quadratic for x in terms of v
0
and
θ
. If the ball is launched at an
angle rather than horizontally the knowledge of v
0
and the angle
θ
still permits the range
to be calculated.
APPARATUS
SAFETY GLASSES, Projectile launcher and kit, Plumb bob, 2 meter
sticks, Carbon paper, White paper, C clamp, Computer, ULI timer and Gate Timing
(projectile) program.
INITIAL SET-UP

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