Applied Physics I: Chapter 1: Properties of Matter - Elasticity
Experimental Determination of Youngs modulus - Non uniform Bending
It consists of a beam, symmetrically supported on the two knife edges A and B. A weight hanger is suspended at the centre (C) of the beam my means or a loop (or) thread.
EXPERIMENTAL
DETERMINATION OF YOUNGS MODULUS - NON UNIFORM BENDING
STATICAL METHOD
Description:
It
consists of a beam, symmetrically supported on the two knife edges A and B. A
weight hanger is suspended at the centre (C) of the beam my means or a loop
(or) thread. A pin is fixed vertically at 'C' by some wax as shown in Fig 1.14.
In order to focus the tip of the pin a travelling microscope (M) is placed in
front of this arrangement.
Procedure:
Taking
the weight hanger as the dead load (W) the microscope is adjusted and the tip
of the pin is made to coincide with the horizontal cross wire. The reading is
noted from the vertical scale of the microscope.
The
weights are added (loaded) in steps of m, 2m, 3m kilograms and the
corresponding readings are noted from the vertical scale of the microscope. The
same procedure is repeated while unloading and the readings are tabulated in
the tabular column as shown. The mean depression 'y' is found for a load of M
kg.
Theoretically,
we know the depression produced is
.....(1)
Where
‘l’ be the length of the beam (i.e.)
the distance between the knife edge. If 'b'
is the breadth of the beam and 'd' is
the thickness of the beam, then
The
geometical of moment of inertia Ig = bd3 / 12 ...(2)
Also
the weight W = Mg ...(3)
Substituting
eqn.(2) and eqn.(3) in eqn.(1), we get
Rearranging
eqn. (4) we get
Youngs
modulus
.....(5)
Substituting
the mean value of (M/y), from the tabular column, the youngs modulus Y can be
determined.
Graphical Method (or) Dynamical Method:
A
graph is drawn taking load. 'M' along x
axis and depression (y) along y axis. It will be a straight line as shown in
Fig.1.15. The slope of the graph gives the value of y/M. Eqn.(5) can be written
as Y = gl3/4bd3
. 1/slope
Substituting
the slope value in the given formula the youngs modulus can be calculated.
Applied Physics I: Chapter 1: Properties of Matter - Elasticity : Tag: Applied Physics : - Experimental Determination of Youngs modulus - Non uniform Bending
Applied Physics I: Chapter 1: Properties of Matter - Elasticity
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