Al-Hadba University College
Practical Medical Physics
Prof. Dr. Saeed Hassan
Experiment-1
Determination of Gravity Acceleration using Simple Pendulum
Objective
1 –Study of the simple harmonic motion of the simple pendulum.
2- Investigation the relationship between periodic time
and the length of the pendulum string
3- Determination the Earth’s gravitational acceleration
.
Apparatus
Small ball (weight), String, Stopwatch, Metric ruler, Stand with a clamp.
Theory
Simple harmonic motion is a motion that repeats itself over a constant period. Examples of simple
harmonic motion are the motion of a simple pendulum and the motion of a block suspended by a
spring.
The simple pendulum is a small mass (ball) suspended vertically by a thin string that has no mass
and is not stretchable. The ball hanging on the string is in an equilibrium position under the influence
of two forces equal in magnitude and opposite direction, namely the body's weight (the gravity force
acting on the body downward), and the tension force of the string upward. When the ball is displaced
at a slight angle
of no more than 10 degrees and left to move freely, the ball is no longer
balanced and the gravitational force
on it is resolved into two components. One is
,
which is equal to the string tension
force inclined to the column at an angle (θ) in the opposite
direction, and the other component is
which moves the ball toward the equilibrium
position. This component is called a “Restoring force
”, and its direction is always toward the
equilibrium position.
Simple harmonic motion(SHM): is an oscillatory motion in a straight line in which the restoring
force acting on the object is directly proportional to the displacement from the equilibrium position
and acts in a direction opposite to the displacement which is always towards the equilibrium
position.
Periodic Time (T): is the time of one complete oscillation
Amplitude (A): is the maximum displacement from the equilibrium position
In SHM, the velocity of the object is maximum
at the equilibrium position and zero
at the maximum displacement
on both sides, and it acts toward the equilibrium
position at any point during the motion. On the other hand, the acceleration of the object is directly
proportional to the displacement from the equilibrium position. It equals zero
at the
equilibrium position and maximum
at the maximum displacement
on both sides,
and is directed towards the equilibrium position.
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Al-Hadba University College
Practical Medical Physics
Prof. Dr. Saeed Hassan
It is called a simple pendulum when the displacement
of the vibration (i.e. the amplitude of the
motion) is almost constant and does not change with time. This can be obtained by making the
displacement angle very small, less than 10 degrees so that the
can be considered equal to
the angle
itself that
.
According to this, the relationship for calculating the periodic time of oscillation time
deduced and equal to:
√
was
……………… (1)
Squaring both sides, the acceleration of gravity
can be obtained in a unit of
or
as:
.….………….. (2)
where : Periotic time (time of one oscillation) ;
: The length of the pendulum string .
Fig. (1): Simple Pendulum
Method:
1- Fix the pendulum at the top of the stand so that the length of the string from the point of swing
to the center of the ball is approximately 100 cm.
2- Shift the pendulum ball a small horizontal distance from its equilibrium position of an angle no
more than 10 degrees, then allow it to oscillate for considered displacement.
3- Calculate the time of 20 oscillations with a stopwatch, let it be t seconds, then repeat the
process and take the average of the time (
.
4- Shorten the length of the string by 10 cm and each time find the value of 20 oscillations until
you obtain different values for the length
of the pendulum.
5- Find the time of one oscillation by dividing the average time of oscillations by 20,
for all lengths, then take the square of the time of one oscillation
as
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Al-Hadba University College
Practical Medical Physics
Prof. Dr. Saeed Hassan
6- Record your readings and results in a table as below.
Pendulum
string length
L (cm)
Time of 20 osc. (sec)
Time of one osc.
(s)
(s2)
7- Plot graphical relationship between the length of the pendulum (L) on the y-axis and the square
of the periodic time
on the y-axis. The find the slope of the resultant straight line that
passes through the origin.
……………… (3)
8- From this relationship we find the acceleration of gravity
as follows:
Then from equation (2) we get:
………………. (4)
Questions
1- Define simple harmonic motion.
2- What is the required condition for the harmonic motion to be simple?
3- In a simple pendulum, in which direction does the velocity always point?
4- The velocity of the pendulum is maximal at the ……………… point, and zero at the ……………
point.
5- The acceleration of the pendulum is …………. at the equilibrium point and ………… at the
greatest displacement point.
6- Is the total energy (= kinetic + potential) of the pendulum constant or changeable when air
resistance is ignored? When air resistance is taken into consideration, what is the total energy?
7- How does the periodic time of oscillation of a simple pendulum change with:
a- pendulum length,
c- ground acceleration,
b- pendulum ball mass,
d- pendulum ball volume
8- If the periodic time of the pendulum is 2 seconds, use g=980 cm/s2 to calculate the length of the
pendulum.
9- Does the gravitational acceleration change with rise and fall from sea level and why?
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