Experiment 5 – RATE OF ACCELERATION DUE TO GRAVITY
Because of the lack of proper measuring tools, Galileo did not use the Leaning Tower of Pisa
as is often illustrated to determine that all objects regardless of mass will fall to the earth at the
same rate of acceleration. Instead he used an inclined plane on which he rolled balls and
measured the time it took to for the ball to pass a measured distance. Later the same results were
obtained by use of a pendulum which Galileo reasoned was a constantly falling object. The rate
of fall of an object was found to increase with time, according to the equation: d = 1/2at 2, and
a = 2d/t2, where d = distance, a = acceleration, and t = time. When air resistance is insignificant,
“a” is equal to “g”, the gravity constant. Near the earth’s surface, g = 9.8 m/s2.
When analyzing the movement of a pendulum, “g” is calculated by an equation that is
specific for pendulum motion – g = 4 π2L/t2 , where L = the length of the pendulum. Thus,
g = 39.4 L/t2. Notice the similarity of the pendulum equation to the general equation shown
above: a = 2d/t2.
To determine the acceleration of a falling object due to gravity
– To understand the concepts of acceleration and gravity in a pendulum system
The required equipment includes: ring stand and clamp (alternately, pencil and tape, as
shown here), string with attached hook at one end, large metal washers, stop watch, and meter
A: The Pendulum Motion
Open a paper-clip into a kind of hook and tie one end to a length of string. Hook one washer
onto the other end of paper-clip. The other end of the string will be attached to a support, which
is either the prong of a clamp mounted on a ring stand and extending outward into the aisle space
or (as shown above) a pencil taped to the bench, where about half of the pencil extends outward
into the aisle space. Tie the upper loop so that the length (L) from the bottom of the support
(prong or pencil) to the “center” of the washer is approximately one half meter; i.e., 49.0 -51.0
cm (equal to 0.490 – 0.510 m), measured with a meter stick to the nearest 0.1 cm. Record below.
Pull the pendulum back to a position about 45 degrees from vertical (as in above picture),
and without pushing, release and let the pendulum swing freely for exactly one minute (60
seconds). [If the washer hits the lab bench or other object, start the run again]. One lab partner
should count the swings and another partner should time the run. A full swing is one out and
back, and a half-swing is out-but-not-back from the release point. Count each complete swing,
and if it has occurred at the 60 seconds mark, a half swing. Record the number of swings to one
decimal place (e.g., as 20.0, or 20.5 swings). Do this procedure at least three times to obtain an
average number and as accurate a count as possible.
L = __________ cm
Number of swings (1 washer):
Convert from centimeters to meters: L = _________ m .
______ _______ _______
Time of one swing = 60 seconds
Average # of swings
Acceleration = 39.4 L = __________m/s2
(for 1 washer)