Answer to Question #125880 in Physics for Hum

Question #125880
3. An iron rod 4 m long and 0.5 cm2 in cross-section stretches 1 mm when a mass of 225 kg is hung from its lower end. Compute Young's modulus for the iron.
1
Expert's answer
2020-07-13T11:44:52-0400

The relation between stretch and load is given by the Hooke's law:


mgA=YΔLL\dfrac{mg}{A} = Y\dfrac{\Delta L}{L}

where m=225kgm = 225kg is the mass of the load, g=9.81m/s2g = 9.81m/s^2 is the constant, ΔL=1mm=103m\Delta L = 1mm = 10^{-3}m is the strech, L=4mL = 4m is the length of the rod, A=0.5cm2=0.5104m2A = 0.5cm^2 = 0.5\cdot 10^{-4}m^2 and YY is the Young's modulus.

Expressing the Young's modulus, get:


Y=mgLAΔL=2259.8140.5104103=176.58109Pa=176.58GPaY = \dfrac{mgL}{A\Delta L} = \dfrac{225\cdot 9.81\cdot4}{0.5\cdot 10^{-4}\cdot 10^{-3}} = 176.58\cdot 10^9Pa = 176.58GPa

Answer. 176.58 GPa.


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