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stress, strain, deformation and g

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Please find attached 8 mechanics problems involving wires and planets.

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Solution Summary

A few problems related to elastic deformation are solved. Here deformed objects are concrete post and metal wire.

A problem related to estimation of value of g at another planet, based on simple pendulum oscillations observations, is solved.

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1.
diameter (D) = 32 cm == 0.32 m
length (L) = 3 m
load (F) = 9600 kg == 9600*9.8 N

cross-sectional area, A = pi*D^2/4 = 3.1415*0.32^2/4 = 0.0804 m^2

a.
Stress (sigma) = F/A = 9600*9.8/0.0804 = 1170149.254 N/m^2 --Answer

b.
Modulus of elasticity for concrete (E) = 3*10^7 N/m^2 (I have taken in this value based on an idea that generally concrete modulus of elasticity varies in range of 30-50 GPa)

Because, by Hook's law,
Stress (sigma) = Modulus of elasticity(E) * Strain(epsilon)
Strain (epsilon) = sigma/E = 1170149.254/(3*10^7) = ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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