3B SCIENTIFIC PHYSICS 8405740 Instrucciones De Uso página 6

4. Additionally required
For setting up:
1 H-shaped base
3 Stand rods, 750 mm, 12 mm Ø
1 Square clamp
1 Rod with hook
For dynamic measurements:
1 Stopwatch
5. Sample experiments
5.1 Static measurement in the elastic range
•
Set up experiment as in Fig. 1.
•
Set up circular scale and chuck opposite its
counter-bearing and at the same both beaings
are aligned horizontally and that the orienta-
tion towards the opposing chuck is accurate.
•
Secure torsion rod into both chucks without
twisting it. Adjust the H-shaped base to the
correct length for this.
•
Calibrate the zero point for the angular scale
by slightly loosening the knurled screw on the
counter-bearing and rotating the rod. Tighten
knurled screw again.
•
Fasten pulley to stand rod. Make sure that the
pulley is in the same vertical plane as the circu-
lar scale.
•
Suspend the spring dynamometer over the
pulley using the square clamp and the rod with
a hook.
•
Fasten hemp string to circular scale, thread
through the groove and around the pulley, and
fasten to spring scale.
•
Increase the force acting on the circular scale
(i.e., the torque) in 0.1 N steps by shifting the
pulley along the stand rod and read the result-
ing angle of twist or torsional angle.
•
Plot a graph of torsional angle and torque.
The experiment set-up guarantees that the force
will always act vertically, since the string runs at a
tangent to the circular scale. This means the simple
equation
= ⋅
M F r
can be used to calculate the effective torque.
It is imperative that the force is not increased too
much in order not to exceed the elastic range of
deformation (different from material to material).
If the circular scale returns to zero after relieving
the force, the elastic range has not been exceeded.
Within the elastic range, the effective torque M is
proportional to the torsional angle ϕ. This relation
can be described as follows:
M
The proportionality factor D
constant or torsion coefficient. This physical torsion
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coefficient depends on the material and the dimen-
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sions of the wire. It can be derived from the slope
of the line in the diagram, or the quotient of
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torque M and the torsional angle ϕ, respectively:
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D
W
The torsion coefficient D
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with the length of the wire, as well as with its di-
ameter.
5.1.1 Determining the limit of elasticity (yield
•
•
•
If the circular scale does not return to an angle of
0° after relieving the force and some slight defor-
mation remains, then the limit of elasticity, the
yield point, has been passed.
The resulting torsional angles and torques depend
on material and geometry (length and diameter of
the wire investigated).
Once the limit of elasticity has been exceeded, the
measured values do not follow a straight line any-
more. Plastic (permanent) deformation of the wire
results.
5.2 Static measurement in the plastic range –
•
•
•
Even when the force is removed entirely, an angle
of twist is still observed. The wire has been physi-
cally deformed by a corresponding degree.
•
•
In order to get back to the 0° mark (original posi-
tion) now, an extra counteracting force is required.
•
2
= ϕ ⋅
D .
W
= M/ϕ
w
point)
Set up the torsion apparatus as in 5.1.
By moving the pulley, increase the force in
steps of 0.1 N and read off the resulting tor-
sional angles.
Each time the force is increased, release the
force on the circular scale by taking away the
dynamometer and check that the the scale re-
turns to an angle of 0°.
mechanical hysteresis
Set up the torsion apparatus as in 5.1.
By moving the pulley, increase the force in
steps of 0.1 N and read off the resulting tor-
sional angles.
After obtaining a torsional angle of 180°, start
to decrease the force, again in steps of 0.1 N.
Now reverse the direction of the string around
the circular scale, so that the force is exterted
by the dynamometer in the opposite direction.
Once more, increase the force in steps of 0.1 N
and read off the resulting torsional angles.
Deform wire, step by step, up to a torsional
angle of -180°.
is called the torsional
w
of a material decreases