explain the cantilever experiment?
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In this experiment we try to measure the Elasticity modulus of scales
made of different materials with the cantilever beam arrangement.If we con-
sider the beam in the position given in the figure below
We define coordinate z along the length of the beam, coordinate y vertically
from the centerline of the beam and coordinate x widthwise across the beam
so as to complete a right handed system. Beam deflections (in the y direc-
tion) are denoted using the variable ν which in general will be a function of
z , i.e. ν = ν(z). The bending moment Mx(z) is positive if the upper fibers
of the beam are in compression and the bottom fibers are in tension.
For a symmetric cross section beam made of a linear elastic material,
whose displacements and slopes under load are small relative to its unde-
formed configuration, the relationship between the displacement and bend-
ing moment is
EI{−d
2ν
dz2
} = Mx
where EI designates the bending moment of the beam; E is the modulus of
elasticity and I is the second area moment of the cross section (L
4
) about
the x-axis. For a rectangular cross section I =
bh3
12 . We can get the relation
after some manipulation as
ν =
mgz2
(3l − z)
6EI
From which if z ' L we get, for
E =
4mgl3
bh3ν
made of different materials with the cantilever beam arrangement.If we con-
sider the beam in the position given in the figure below
We define coordinate z along the length of the beam, coordinate y vertically
from the centerline of the beam and coordinate x widthwise across the beam
so as to complete a right handed system. Beam deflections (in the y direc-
tion) are denoted using the variable ν which in general will be a function of
z , i.e. ν = ν(z). The bending moment Mx(z) is positive if the upper fibers
of the beam are in compression and the bottom fibers are in tension.
For a symmetric cross section beam made of a linear elastic material,
whose displacements and slopes under load are small relative to its unde-
formed configuration, the relationship between the displacement and bend-
ing moment is
EI{−d
2ν
dz2
} = Mx
where EI designates the bending moment of the beam; E is the modulus of
elasticity and I is the second area moment of the cross section (L
4
) about
the x-axis. For a rectangular cross section I =
bh3
12 . We can get the relation
after some manipulation as
ν =
mgz2
(3l − z)
6EI
From which if z ' L we get, for
E =
4mgl3
bh3ν
Answered by
1
Introduction
1. Brief description
A plastic optical fiber is attached to a (cantilever) beam to monitor its deflection. The change in the light intensity of the optical fiber is monitored using a light-dependent resistor (LDR) and a basic voltage divider circuit. The output of the LDR is continuously measured by the ADC-16 and this simple system is able to provide real-time beam deflection monitoring with a PC.
2. What the experiment is trying to teach
The experiment highlights the potential use of an optical fiber as a sensor for monitoring, in real time, the deflection of a structure. Students will also gain practical experience in building up a basic electrical circuit based on simple devices such a light-dependent resistor (LDR), reading resistor values, principle of voltage dividers and Ohm’s law.
3. Prior knowledge required
Students need to have an idea of how an optical fiber transmits light through its core and the principle of total internal reflection (TIR) and the effect of excessive bending on the light transmission in these light-guiding media. Secondly, students should have some appreciation of the function of a light-dependent resistor, the principles of voltage dividers and Ohm’s law.
4. Target group
This experiment is suitable for students taking Advanced Physics and serves as a simple introduction to the practical use of optical, electronic and optoelectronic devices.
1. Brief description
A plastic optical fiber is attached to a (cantilever) beam to monitor its deflection. The change in the light intensity of the optical fiber is monitored using a light-dependent resistor (LDR) and a basic voltage divider circuit. The output of the LDR is continuously measured by the ADC-16 and this simple system is able to provide real-time beam deflection monitoring with a PC.
2. What the experiment is trying to teach
The experiment highlights the potential use of an optical fiber as a sensor for monitoring, in real time, the deflection of a structure. Students will also gain practical experience in building up a basic electrical circuit based on simple devices such a light-dependent resistor (LDR), reading resistor values, principle of voltage dividers and Ohm’s law.
3. Prior knowledge required
Students need to have an idea of how an optical fiber transmits light through its core and the principle of total internal reflection (TIR) and the effect of excessive bending on the light transmission in these light-guiding media. Secondly, students should have some appreciation of the function of a light-dependent resistor, the principles of voltage dividers and Ohm’s law.
4. Target group
This experiment is suitable for students taking Advanced Physics and serves as a simple introduction to the practical use of optical, electronic and optoelectronic devices.
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