Calculate Young\'s Modulus from the following data: Load on the hanger (gm) Read

Question

Calculate Young's Modulus from the following data:

Load on the hanger (gm)

Readings of the scale (cm)

Change in the reading
of the scale when the
load is increased
by M = _____ gm

Load increasing (si)

Load decreasing (sd)

Average s

100

-8.4

-8.5

300

-6.2

-6.3

x1 = s4 - s1 =

500

-3.9

-4.0

x2 = s5 - s2 =

700

-1.7

-1.8

x3 = s6 - s3 =

900

0.5

0.4

1100

2.7

2.6

Average x =

Average diameter of the wire = 0.036 cm

Average length of the wire = 96.7 cm

Average diameter of the cylinder = 1.24 cm

Average distance between the mirror and the scale = 84.6 cm

g = 980 cm/s2

Notes: In your answer give average scale readings as s = {s1, s2, s3, s4, s5, s6} and change in scale readings as x = {x1, x2, x3}. Use CGS units

Load on the hanger (gm)

Readings of the scale (cm)

Change in the reading
of the scale when the
load is increased
by M = _____ gm

Load increasing (si)

Load decreasing (sd)

Average s

100

-8.4

-8.5

300

-6.2

-6.3

x1 = s4 - s1 =

500

-3.9

-4.0

x2 = s5 - s2 =

700

-1.7

-1.8

x3 = s6 - s3 =

900

0.5

0.4

1100

2.7

2.6

Average x =

Explanation / Answer

s1 = 8.45 m

s2 = 6.25 m

s3 = 3.95 m

s4 = 1.75 m

s5 = 0.45 m

s6 = 2.65 m

s4-s1 = 1.75-8.45 = 6.7cm

strain = e/l = 6.7/96.7= 0.0692

stress = F/A = (0.3*9.81)/(3.142*0.018^2*10^-4) = 2.891*10^7 N

Yong's modulus Y = stress/strain = (2.891*10^7)/0.0692 = 4.17*10^8 N/m^2

1 N = 10^5 dynes

1m^2 = 10^4 cm^2

Y = 4.17*10^11 dynes/cm^2

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