Gravitational Torsion Balance
012–06802B
8
d
b
The enormous strength of the Earth's attraction for the small
masses, in comparison with their attraction for the large masses, is
what originally made the measurement of the gravitational
constant such a difficult task. The torsion balance (invented by
Charles Coulomb) provides a means of negating the otherwise
overwhelming effects of the Earth's attraction in this experiment.
It also provides a force delicate enough to counterbalance the tiny
gravitational force that exists between the large and small masses.
This force is provided by twisting a very thin beryllium copper
ribbon.
The large masses are first arranged in Position I, as shown in
Figure 12, and the balance is allowed to come to equilibrium. The
swivel support that holds the large masses is then rotated, so the
large masses are moved to Position II, forcing the system into
disequilibrium. The resulting oscillatory rotation of the system is
then observed by watching the movement of the light spot on the
scale, as the light beam is deflected by the mirror.
Any of three methods can be used to determine the gravitational
constant,
G
, from the motion of the small masses. In Method I,
the final deflection method, the motion is allowed to come to
resting equilibrium—a process that requires several hours—and
the result is accurate to within approximately 5%. In method II,
the equilibrium method, the experiment takes 90 minutes or more
and produces an accuracy of approximately 5% when graphical
analysis is used in the procedure. In Method III, the acceleration
method, the motion is observed for only 5 minutes, and the result
is accurate to within approximately 15%.
M
E
T
H
O
D
I
:
M
ea
su
r
e
m
e
n
t
by
F
i
n
a
l
D
e
fl
ec
t
i
on
Setup Time: ~ 45 minutes; Experiment Time: several hours
Accuracy: ~ 5%
Theory
With the large masses in Position I (Figure 13), the gravitational
attraction,
F
, between each small mass (
m
2
) and its neighboring
large mass (
m
1
) is given by the law of universal gravitation:
F = Gm
1
m
2
/b
2
(1.1)
where
b
= the distance between the centers of the two
masses.
Large Masses:
Position I
Large Masses:
Position II
Figure 13
Origin of variables
b and d
➤
Note:
5% accuracy is possible in
Method I if the experiment is set up on a
sturdy table in an isolated location
where it will not be disturbed by
vibration or air movement.
➤
Note:
5% accuracy is possible in
Method II if the resting equilibrium
points are determined using a graphical
analysis program.
Summary of Contents for AP-8215
Page 24: ......