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Single Cantilever

The document outlines an experiment to determine Young's modulus of a material using a single cantilever setup. It includes the aim, required apparatus, relevant formulas, theoretical background, and a detailed procedure for conducting the experiment. The results section indicates that the Young's modulus will be calculated based on the measurements taken during the experiment.

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958 views3 pages

Single Cantilever

The document outlines an experiment to determine Young's modulus of a material using a single cantilever setup. It includes the aim, required apparatus, relevant formulas, theoretical background, and a detailed procedure for conducting the experiment. The results section indicates that the Young's modulus will be calculated based on the measurements taken during the experiment.

Uploaded by

raju555500002222
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Single Cantilever

Aim

To determine Young’s modulus of the given material using single cantilever.

Apparatus required

Material beam, meter scale, vernier calliper, screw gauge, slotted weights, and trav-
elling microscope.

Diagram

Figure 1:

Formula used
4M gL3
Young’s modulus q = 3
N m−2
bd δavg

where M – Mass required to produce an elevation δ.


L – Distance from the fixed support to free end.
b – Breadth of the scale.
d – Thickness of the scale.
δ – Elevation produced for the load M .

Department of Physics, MUSE, Mysuru Expt. 1 : 1 of 3


Single Cantilever

Theory

Young’s modulus is defined as the ratio of the longitudinal stress to the longitudinal
starin within the elastic limits. A material whose Young’s modulus is high is consid-
ered as rigid. Hooke’s law (stress is directly proportional to strain) holds good in the
elastic range. It is a measure of stiffness of the elastic material.
Longitudinal stress
Young’s modulus =
Longitudinal strain

Tabular column

Least count of the travelling microscope:

Value of 1 MSD
LC = cm.
Total Number of VSD

Load Increasing (LI) Readings

Load (M ) in gm MSR in cm CVD T R = M SR + (CV D × LC) in cm

Load decreasing (LD) Readings

Load (M ) in gm MSR in cm CVD T R = M SR + (CV D × LC) in cm

To find δmean
Load (M ) in gm LI LD Average

Department of Physics, MUSE, Mysuru Expt. 1 : 2 of 3


Single Cantilever

Load (M ) in gm R1 Load (M ) in gm R2 δ = R1 ∼ R2

δavg = —–cm

Calculations

Distance between the two knife edges L = 60 cm


Mass for which elevation is found M = 100 g
Breadth of the bar b = 2.5 cm
Thickness of the bar d = 2.78 mm.

Procedure
1 The material of the given bar whose Young’s modulus is to be determined is
fixed to a rigid suuport at a distance of L = 60 cm.

2 The bar is loaded with 50 g at one end using weight hangers.

3 A pin is fixed at the midpoint of the beam. It is focussed through a microscope


and the reading is noted.

4 Increase the load on the scale pan in steps of 50 g, till a maximum load of 200 g
and the corresponding TM reading are noted in each case.

5 The procedure is repeated by decreasing the load in steps of 50 g.

6 Calculate the mean elevation for 100 g.

7 Calculate the Young’s modulus using the given formula.

Result

The Young’s modulus of the material of the given bar =——— N m−2 .

Department of Physics, MUSE, Mysuru Expt. 1 : 3 of 3

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