Investigation on Young Modulus

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  • Topic: Young's modulus, Vernier scale, Measurement
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Samarpan Rai
30/11/012
Physics HL

Investigation on Young Modulus

Young's modulus, also known as the tensile modulus, is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. Young's modulus is named after Thomas Young, the 19th century British scientist. It is a very important concept that categorizes metals on basis of their elasticity. In the last lab, we were asked to find out the Young Modulus of two wires: Copper and Steel. I worked on Copper wire. My hypothesis on the report was that “The Young Modulus of a wire is directly proportional to the extension possible by the object.” Which means, the more a wire stretches from its original position the more will be its Young Modulus. It is because, F = -kx, and –k should be that constant.

We were given some wires which were fixed on ceiling of lab on one end and other end had vernier caliper like measurement device. My controlled variable was the diameter of Wire, Length of wire and acceleration due to gravity (g = 9.8 ms-2) and independent variable was the load that can be applied to the string, which were given in the form of 0.5 kg blocks and had constant mass. Extension of string was the dependent variable and it was measured with a vernier caliper with the accuracy of 0.001mm.

The equation of Young modulus is:
Young modulus (e) = StressStrain
⇒ e = F. L∆L. A
Transforming in the form of straight line, y = mx
∆L = LA. e. F

Where,
F = Force applied
L = Original length of wire
∆L = Extension of wire
A = Cross-section of wire

Apparatus used:
1. Copper wire
2. Vernier Caliper
3. String
4. Measuring tape
5. Holding weight
6. Micrometer
7. Mass block
Procedure:
Two wires were hung from the ceiling. One was for supporting and other for measurement. 1. The supporting wire is to be fixed with a load to prevent disturbances from movement during the experiment. 2. The length and diameter of experimental wire is to be measured. 3. The supporting wire should br attached with the main scale of vernier caliper and experimental wire with vernier scale. 4. The vernier scaled had a hole in end where load was hung with each measurement the load was increased by 0.5 kg. 5. The reading should be made each time from the main scale and vernier scale. The vernier scale helped to increase the precision. 6. The load was increased till 0.5kg and reading was made twice i.e. Once loading and other unloading.

Data processing:
Length of wire (L): 198.6 cm ± 0.05 cm = 1.986m ± 0.00005 m % error in length = 0.000051.986 x 100% = 2.52 %
Diameter of wire: 0.99 mm ± 0.01 mm = 0.00099 m ± 0.00001 m So, radius = 0.000495m ± 0.000005m
And, Cross-section (A) =πr2
=π (0.000495) 2
= 7.7 x 10-7 m2
% error of Cross section (A) = 2 0.0000050.00099 x 100%
= 1.01 %
Thus, A = 7.7 x 10-7 m2 ± 7.8 x 10-9 m2
Total error in controlled variable = (1.01 + 2.52) % = 3.53 % Data obtained after experiment:
SN| Load/kg ± 0.5 kg| Load/N±4.9N| Length of wire/mm ± 0.05mm| Extension/mm ± 0.1mm| Average/mm ± ∆A mm| | | | Load| Unload| Load| Unload| |
1.| 0| 0.00| 0.20| 1.3| 0.00| 0.00| 0.00± 0.0|
2.| 0.5| 4.91| 0.8| 2.4| 0.60| 1.1| 0.85± 0.5|
3.| 1.0| 9.82| 1.4| 2.7| 1.2| 1.4| 1.3± 0.2|
4.| 1.5| 14.7| 1.7| 3| 1.5| 1.7| 1.6± 0.2|
5.| 2.0| 19.6| 2.1| 3.2| 1.9| 1.9| 1.9± 0.0|
6.| 2.5| 24.55| 2.4| 3.4| 2.2| 2.1| 2.1± 0.1|
7.| 3.0| 29.5| 2.8| 3.5| 2.6| 2.2| 2.4± 0.4|
8.| 3.5| 34.4| 3.2| 3.8| 3.0| 2.5| 2.7± 0.5|
9.| 4.0| 39.3| 3.7| 4| 3.5| 2.7| 3.1± 0.8|
10.| 4.5| 44.2| 4.0| 4.1| 3.8| 2.8| 3.3± 1.0|

Using technology the gradient of line of best of best fit is 0.608 but since the reading of extension is in mm, Slope of line of best fit (M) = 0.0608 x 10-3 = 6.08 x 10-5. The slope of upper-worst fit line:

(x2,y2) = (43,4.2)
(x1,y1) = (41,4)
Slope (M)...
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