PASCO AP-8215, Инструкция по эксплуатации, Страница: 16 / 24

Gravitational Torsion Balance 012–06802B
12
geometry for this second force is shown in Figure 17 (the
vector arrows shown are not proportional to the actual
forces).
From Figure 17,
The force, F
0
is given by the gravitational law, which
translates, in this case, to:
and has a component ƒ that is opposite to the direction of
the force
F :
This equation defines a dimensionless parameter, b , that is
equal to the ratio of the magnitude of ƒ to that of F . Using
the equation F = Gm
1
m
2
/b
2
, it can be determined that:
b = b
3
/(b
2
+ 4 d
2
)
3/2
From Figure 17,
Fnet = F - f = F - bF = F(1 - b)
where F
net
is the value of the force acting on each small
sphere from both large masses, and F is the force of
attraction to the nearest large mass only.
Similarly,
G = G
0
( 1 - b)
where G is your experimentally determined value for the
gravitational constant, and G
0
is corrected to account for
the systematic error.
Finally,
G
0
= G/( 1 - b)
Use this equation with equation 1.9 to adjust your
measured value.
F
0
=
Gm
2
m
1
( b
2
+ 4 d
2
)
f =
Gm
2
m
1
b
( b
2
+ 4 d
2
)( b
2
+ 4 d
2
)
1
2
=
β
F
Φ
d
b
F
0
F
f
Figure 17
Correcting the measured value of G
sin
Φ
=
b
( b
2
+ 4 d
2
)
1 2 1 2
f = F
0
sin
Φ