Desmond Mansfield

DETERMINATION OF THE YOUNG MODULUS

01/11/09

me05

Abstract

Introduction

The aim of the experiment was to find the Young's modulus of three different material bars, starting with glass, by measuring how much they bend under a suspended load.

Theory

Young's modulus is defined as stress over strain.

It is the most common modulus used in the analysis of the bending bars and rods. To do this bars are rested upon two knife points and a load is suspended from their center, with the central depression being measured.

It can be shown that

where

In this experiment depression, , and load, , are the measured quantities. If a graph of depression against load is plotted, then it can be shown that the gradient, , is . As L, I and E are constants then the graph will be a straight line and Young's modulus will be easily obtained from basic algebraic manipulation of the formula just given for the gradient.

The main source of experimental error will come from the measurement of various properties of the bars, as these properties enter the final formula raised to powers of 3 and 4.

Method

List of Apparatus

Rods

Knife-Points

Bar

Masses

pan

Clamp stand

Microscope

Needle

Micrometer

Diagram of Experimental set-up

Method

1)Carefully measure the dimensions of the rod with a micrometer (use a ruler for the length), taking an average value of the width.

2)Carefully position the rod on the two knife points, loading the bar in the center with the pan, ensuring that equal amounts protrude over the knife points at each end, as shown in the diagram above.

3)Set up the the clamp stand behind the experiment, and ensure the needle is held tightly in the clamp stand, parallel to the table surface and perpendicular, but just touching, the center of the bar.

4)Load masses gradually, ensuring each time that the bar is symmetrical. It should now be possible to use the microscope to measure the depression of the bar by viewing the new position of the bar against its old position, shown by the needle. Record each result.

5)Unload masses gradually, ensuring each time that the bar is symmetrical. Use the microscope to measure the depression of the bar by viewing the new position of the bar against its old position, shown by the needle. Record each result.

6)Plot a graph of Depression against load, , and from the gradient,

find the Young's modulus of the rod.

7)Compare the found Young's Modulus (including the calculated errors) with accepted values for the material found in a table of material constants. Make a comparison between the found value and the accepted value.

Results

Below are the tabulated results of load (g) against average (mean) depression (cm) – as readings were taken twice for each bar. Whilst the readings were taken randomly as specified they have been tabulated by ascending load for the convenience of the reader. Full tables (un-averaged) can be found in the appendix at the back of this report.

Glass Rod – Circular
Load (g) / average depression (cm)
0 / 0.000
10 / 0.000
20 / 0.000
30 / 0.000
40 / 0.000
50 / 0.025
60 / 0.050
70 / 0.050
80 / 0.050
90 / 0.050
100 / 0.100

Brass road – circular
Load (g) / average depression (cm)
0 / 0.000
10 / 0.050
20 / 0.075
30 / 0.125
40 / 0.150
50 / 0.225
60 / 0.250
70 / 0.275
80 / 0.300
90 / 0.375
100 / 0.425
110 / 0.450
120 / 0.500
130 / 0.575
140 / 0.575
150 / 0.625
160 / 0.675
170 / 0.700
180 / 0.750
190 / 0.800
200 / 0.825

Balsa – rectangular
Load (g) / average depression (cm)
0.00 / 0.000
10 / 0.150
20 / 0.325
30 / 0.475
40 / 0.575
50 / 0.750
60 / 0.900
70 / 1.300
80 / 1.450
90 / 1.375
100 / 1.525
110 / 2.175
120 / 1.825
130 / 1.975
140 / 2.125
150 / 2.225

•Results (this section has to include the final results of the analysis, i.e. the coefficients

and the errors produced by the three methods. This section will also contains the data

table and the plot (from the computer fitting). All calculations and the manual graph

plotting results will be made in the labbook***. The later will also contain the exercises on

the error propagation.)

•Discussion (discuss the similarities/differences between the three different mehods of

analysis. Compare the results and their errors, explain the differences. This section should

also contain the answers to the questions given in different sections of the practical.)

•Conclusions. (brief summary of the analysis)

References

“DETERMINATION OF THE YOUNG MODULUS me05” - specimen brief.

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