EXPERIMENT
FREE
FALL
Introduction:
1. Free fall
For uniform acceleration “
a
” (constant in magnitude and direction), the wellknown
kinematic equations of motion can be written as :
v
=
v
o
+ a t
y
−
y
o
=
½
(v
o
+
v) t
y
y
o
=
v
o
t +
½
a t
2
v
2
=
v
o
2
+ 2 a (y
y
o
)
where
y
,
v
, and
a
are the distance, instantaneous velocity and instantaneous acceleration,
respectively. The initial conditions are: at
t = 0, y = y
o
and
v = v
o
.
Whenever the air resistance on a falling object is negligible, the motion is referred to as free
fall
.
Near the earth’s surface, the
acceleration due to gravity
“g”
is nearly constant over the range
of motion and approximately equals
9.80 m/s
2
downward. This value decreases with increasing
altitude and slightly varies with latitude. A freely falling object moves freely under the effect of
gravity regardless of its initial condition. For a freely falling body, the same kinematic equations,
mentioned above, hold true with the substitution
a =
g
.
2. Projectile motion
If a projectile is projected horizontally, it describes an arc as shown in Fig.(1). The
horizontal distance traveled by the projectile
x
is called the
“range”
. The vertical distance of the
falling projectile is
y
. The initial conditions of the motion are: at t = 0, the horizontal component of
the velocity is
v
xo
and the vertical component
v
yo
= 0
. The acceleration is uniform i.e. constant and
downward and has the value
g
, the acceleration due to gravity. From the kinematic equations of
motion, we can get the equation of the path:
v
yo
=0
v
xo
y = g x
2
/ 2 v
xo
2
x
The path is a parabola with its vertex at
y
distance
v
x
the original point where the object starts
of
its motion .This equation relates (1) the
fall
v
y
v
acceleration
due
to
gravity
g
,
(2) the
range
x
, (3) the distance of fall
y
, and
Range,
x
(4) the initial velocity
v
xo
.
y
Fig.(1) Range and fall
of a projectile
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View Full DocumentExercise 1:
The equation of motion for a body freefalling from rest can be expressed as
y =
½
g t
2
,
where y is the distance the object has traveled from its starting point, g is the acceleration due to
gravity, and t is the time elapsed since the motion began. In this experiment, you will find an
estimate to g by carefully timing the fall of a steel ball from various heights.
Setup and Operation:
y
Dowel Pin
(Press here)
Release Plate
Thumbscrew
Contact screw
Receptor Pad
Fig. (2) Equipment Setup
9 V DC Adaptor
To the Ball Release Mechanism
Receptor Pad
Time
To 120 VAC, 60 Hz or
220/240 VAC, 50 Hz
(1)
Clamp the ball release mechanism to a lab stand,
or any other device that will hold it vertical and
at the desired height over the floor or table, as
shown in figure 2. For best results, the drop
height y should be 1.5 – 2.0 m. Shorter heights
will work fine, but accuracy is reduced
proportionally.
(2)
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 Spring '11
 WagihGhobriel
 Acceleration, Kinematic equations, ball release mechanism

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