Experiment 3 – Young\'s Modulus of a Wire PDF

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Experiment 3 – Young’s Modulus of a Wire Aims: 1. To determine the Young’s modulus of a steel wire.

Theory:

Figure 1: Stretching of a wire If we apply a force, F, to the end of a wire of initial length l and cross-sectional area A, producing a strain, Δl l , theory predicts that provided the elastic limit is not exceeded:

F Δl where E = Young’s Modulus. =E l A The equation can be rearranged to:

F=

EA ⋅ Δl l

If the Force (F) is applied by hanging a mass (m) on the wire, then F = mg By measurement of the extension of the wire and through the geometry of the testing apparatus, the extension of the wire ( Δl ) can be determined and thus – the strain can be calculated for the application of each new mass. Using your knowledge of engineering principals, the Stress can also be determined for each of the masses applied. As such the Young’s Modulus of the material can be determined. Young’s Modulus, E =

Stress Strain

Procedure: 1. The apparatus should be set up as in the diagram below (Figure 2). Adding masses to the weight carrier causes the wire to extend rotating the pulley and pointer. From the pointer rotation the extension of the wire can be determined. 2. Measure the radius of the pulley (r). Measure the length of the pointer from the centre of the pulley (R). Measure the length of the wire (l). See schematic set-up in Figure 2. Using the information recorded: Δl =

r ⋅D # R

3. With just the weight carrier hanging on the wire, centre the pointer.# # 4. Measure the diameter of the wire (d). Use the micrometer and repeat your measurements at several places along the wire to obtain an average value.

5. Calculate the cross-sectional area of the wire: A =

πd2 4

Figure 2: Schematic diagram of wire tension apparatus 6. Add masses to the weight carrier and note the pointer deflection (D). Repeat for each weight addition. Then record all changes in deflection as the weights are also removed from the testing apparatus.

Mass$ Added$ (kg)$

7. Record your measurements in the table below: Pointer$Deflection,$D$(mm)$ Extension$of$ Force$ the$Wire$$ (N)$ Adding$ Removing$ Average$ (mm) Δl $

Strain$$$$$$$$$

e=

Δl $ l

Stress$(MPa)$

0.0$

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1.0$

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1.5$

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2.0$

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8. Graph the stress against strain and determine the slope of the graph. 9. Determine the Young’s Modulus of the wire.

Results and Reporting: 1. Tabulate the calculated and experimental results. Also, report the reasons for any large discrepancies. 2. Graph the stress against strain and determine from the graph the Young’s modulus of the material. Present the required graphs (One for mass adding and one for mass removing). Please ensure the formula for the line and the R2 value are presented. 3. Explain clearly (with diagrams where appropriate), how the measurements show the (tensile or compressive) strains. 4. Produce a concise laboratory report. This should include the aims, theory, procedure and results. Clearly present the graphs used to determine the Young’s modulus of the material as well as your determined value for the Young’s modulus. Please investigate what the expected Young’s modulus of the material should be and report on any discrepancies between the observed and expected results. 5. Please note, your laboratory report will be due by 4pm, 1 week after your scheduled lab session...