3B SCIENTIFIC PHYSICS U40205 Instructions D'utilisation page 14

4.8 Evaluation
4.8.1 Determining the point of equilibrium
•
The equilibrium position
from the first five maximum deflections after the
initial movement to position 2 by means of the
following equation:
( ) ( )
⎛
α + α
1 3
1
⎜
α = ⋅
⎜
1
2 3
⎝
•
Use the cursor to mark the maxima and minima
of the curve and read off the values in the "Data"
field on the information bar (see Fig. 7).
Alternatively, the values can be taken from a
spreadsheet prepared using Microsoft Excel if the
results have been saved in this format beforehand.
•
Work out the new equilibrium position
moving the beam to position 3 in a similar way.
4.8.2 Determination of gravitational constant G
m = Mass of small speheres
r = Distance of spheres from axis of rotation
M = Mass of large spheres
M = Mass of inner support beam
B
L = Length of inner support beam
B
W = Width of inner support beam
B
b = Distance between large and small spheres
T = Period of oscillation
k = Angular constant
Δα = Difference between equilibrium points α1 – α2
α1
α3
α5
α4
α2
Fig. 7 Determination of equilibrium points
α
can be calculated
1
( ) ( ) ( )
⎞
+ α α + α
5 2 4
⎟
+
⎟
2
⎠
α
2
The moment of inertia of the torsional pendulum J
given by the sum of the moments of inertia of the
small spheres J and of the inner beam J
= ⋅ ⋅
2
J 2 m r
1
= ⋅ ⋅
J M
B B
12
= +
J J J
tot B
τ k = Δ ⋅ α
2
⎛ π
⎞
2
=
⎜ ⎟
k J
⋅
⎝ ⎠
T
⋅
m M
τ = ⋅
G 2
2
b
after
By substituting the values and rearranging the
equation as appropriate, the required value G can be
derived.
α1
α3
α5
α4
α2
6
( )
+
2 2
L W
B B
tot
⎛ ⎞
3
⎛ ⎞
⋅ ⎜ ⎟
r b
⎜ ⎟
⋅ −
⎜ 1 ⎟
⎜ ⎟
⎜ ⎟
+
2 2
⎝ ⎠
b 4 r
⎝ ⎠
is
tot
.
B