Page 194 - Physics

Physics for Secondary Schools
physicist, mathematician, astronomer and
philosopher who was closely associated
with the scientific revolution. His
achievements include the fi rst systematic
studies of uniformly accelerated motion,
improvements to the telescope and a variety
of astronomical observations.
Galileo understood that free-fall was
a uniformly accelerated motion. The
problem he faced in studying this motion
was in measuring time. He discovered
that over short distances of a few metres,
free-fall occurs very rapidly. In Galileo’s
days, there were no clocks capable of
accurately measuring very short periods.
Therefore, he used his heart pulse to
measure time in many of his experiments.
Later, he developed a water clock and a
pendulum clock, but none of these were
capable of measuring time precisely. To
overcome this problem, Galileo studied
objects rolling down inclined planes,
which slowed the motion suffi ciently
for accurate measurements to be made.
Figure 8.27 shows a body rolling down
an inclined plane.
Figure 8.27: Body rolling down an inclined
plane
Even using the inclined plane, Galileo
was not able to accurately determine
the acceleration due to gravity. One way
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Physics Form 1 Final.indd 188
in which the value for the acceleration
due to gravity could be determined was
by observing the motion of a simple
pendulum. A pendulum consists of a
bob suspended by a wire or string from
a pivot point. When the pendulum bob is
displaced from its equilibrium position
and released, the pendulum swings back
and forth in periodic motion as shown in
Figure 8.28.
Pivot point
String
Mean position Pendulum bob
Figure 8.28: A simple pendulum
The time for the pendulum bob to swing
back and forth, to complete an oscillation
is called its period, abbreviated as T. When
a pendulum moves forth and back once,
it completes an oscillation. The period of
oscillation of the pendulum depends on
its length, l and the acceleration due to
gravity, g, and given as,
l
T = 2p
g
After rearranging the above equation by
making g the subject and substituting the
value of π you get:
2
4 l
g = T 2
l
g = 39.5 T 2
This is the acceleration due to gravity.
Student’s Book Form One
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