012–06802B
Gravitational Torsion Balance
15
changed, the total force (
F
tota
l
) that is now acting to accelerate
the small masses is equal to twice the original gravitational
force from the large masses, or:
F
total
= 2F = 2Gm
1
m
2
/b
2
(3.2)
Each small mass is therefore accelerated toward its
neighboring large mass, with an initial acceleration (
a
0
) that is
expressed in the equation:
m
2
a
0
= 2Gm
1
m
2
/b
2
(3.3)
Of course, as the small masses begin to move, the torsion
ribbon becomes more and more relaxed so that the force
decreases and their acceleration is reduced. If the system is
observed over a relatively long period of time, as in Method I,
it will be seen to oscillate. If, however, the acceleration of the
small masses can be measured before the torque from the
torsion ribbon changes appreciably, equation 3.3 can be used to
determine
G
. Given the nature of the motion—damped
harmonic—the initial acceleration is constant to within about
5% in the first one tenth of an oscillation. Reasonably good
results can therefore be obtained if the acceleration is measured
in the first minute after rearranging the large masses, and the
following relationship is used:
G = b
2
a
0
/
2
m
1
(3.4)
The acceleration is measured by observing the displacement of
the light spot on the screen. If, as is shown in Figure 19:
Δ
s
= the linear displacement of the small masses,
d
= the distance from the center of mass of the small
masses to the axis of rotation of the torsion
balance,
Δ
S
= the displacement of the light spot on the screen,
and
L
= the distance of the scale from the mirror of the
balance,
then, taking into account the doubling of the angle on
reflection,
Δ
S =
Δ
s(2L/d )
(3.5)
Using the equation of motion for an object with a constant
S
1
S
2
Δ
S
2
2
θ
L
Figure 19
Source of data for calculations in
Method III
Содержание AP-8215
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