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Acceleration due to
Gravity
(RRC3B): => SIMPLE PENDULUM
METHOD 2 - SIMPLE PENDULUM
SECTION 2:
EQUIPMENT NEEDED FOR SIMPLE PENDULUM
Ball Set w/hole F2-L (also called density set)
{option: use a density cylinder)
Scale, Digital DD4-PR
Clamp, Pendulum G3-L
Stop watch K3-L
Protractor C3-L [or Geology Y5-L (with rulers)]
Ring Stand rod, 120 cm
String ~1m
in back of DD6-PR
L4-L (on counter)
Table Clamp, large E2-L
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Setup
Fig 7 pendulum clamp setup
Fig 8. Pendulum clamp
fig 9 spherical
plumb bob
Note: for fig 9. Feed the string thru the hole & then feed the
other end of the string thru the loop at the end.
Fig 10 attachment of plumb bob
String to the pendulum clamp
Note for fig 10. Loosen the black knob and slide the string
between the two flat metal rods, then tighten the knob which
pinches the string thus allowing quick and easy adjustment of
the pendulum’s string length.
FIGURE 2
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THEORY
A pendulum is a freely swinging mass supported from a pivot point. The time it takes the
brass ball (or bob) to swing from position A to B and back to A again is called the period
T of the pendulum. For small angles,   20:
T = 2 L / g Equation 1
4 2 L
g =
T2
Equation 1 is called the small-angle approximation for the period of a pendulum.
PROCEDURE
1. Experimentally investigate the relationship between the length and period of a
pendulum. Using five different lengths (e.g., 0.20, 0.40, 0.60, 0.80, 1.00 m),
determine the average period of a pendulum for each length (keeping mass and the
small angle of oscillation constant) by measuring the time for five oscillations and
dividing the total time by 5. Record the data in Data Table 2.
2. Once found acceptable, a theoretical expression can then be used to determine
experimentally other quantities occurring in the expression. For example, Equation 1
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provides a means for experimentally determining g, the acceleration due to gravity,
by measuring the pendulum parameters of length and period as was done previously.
T = 2  L/G
Squaring both sides of Eq. 1, we have:
T2 
4 2
L
g
Hence, the equation has the form y = ax2, that of a parabola. This can be plotted as a
straight line with the general form y = mx’ by letting L = x and y’ = T2, or plotting T2
on the y axis and L on the x. The line will have a slope of m = 42/g.
3. Plot T2 versus L from the experimental data in Data Table 2, determine the slope of
the graph, and compute the experimental value of g using g  4 x
2
slope
. Record
this in the Laboratory Report and compute the percent error of the result.
Data Table 2
Purpose: To investigate period dependence on length.
L
(m)
Time for 5
swings (s)
T
(s)
T2
(s2)
Slope from graph: ___________________________ (s2 / m )
Experimental value of g, g  4 x
Accepted g = 9.80 m/s2
% ErrorA - E X 100 =
2
slope
__________ (m / s2)
(note: in the Austin/ Round Rock area
g = 9.793 m/s2 )
%
EXAMPLE SAMPLE CALCULATION
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A pendulum 20.0 cm long was pulled to the side, making an angle of about 5o with the vertical
and allowed to swing freely. The time for 100 vibrations was 1 min. 29.53 sec and 1 min. 27.29
sec. The average time was calculated to be 89.66.
The time for one vibration 
89.66 sec
sec
 0.8966 sec
T
100vib
vib
43.1416 0.200m
2
Then g was calculated: g 
Error 
9.82  9.80 m sec 2
9.80 m
0.8966 sec 
2
 9.82 m
sec 2
100%  0.2%
sec 2
CALCULATIONS
Questions
1. It was suggested that the time for several periods be measured and the average
period determined, rather than timing only one period.
What are the advantages of this method?
2. Does air resistance cause the period to be larger or smaller than the theoretical
value? (Hint: Consider what would happen if the air resistance were much greater,
e.g., as though the pendulum were swinging in a liquid.)
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Section 2. the Universal Gravitational constant
𝐺 𝑚1 𝑚2
=
𝑟2
.
F=
m1g
where
ball,
m2
m1
is the mass of the dropped
is the mass of the Earth ~5.972 x 1024
Kg,
r = Earth’s approximate radius 6371 Km, & g is the value
you’ve calculated in this lab.
Find G.
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