Answer to Question #132003 in Physics for Bhakti

Question #132003
A brass rod is 15cm long with a circular cross-section of 2cm. A force of 10kN is applied to the end of the rod parallel to its length. The young's modulus for the rod under compression is 90x10^9 N/m^2. The rod shortens by how many millimetres?
1
Expert's answer
2020-09-09T10:22:22-0400

Young's modulus is


"E=\\frac{\\sigma}{\\epsilon},"


Strain is


"\\epsilon=\\frac{\\Delta l}{l}=\\frac{\\sigma}{E}."

The stress is


"\\sigma=\\frac{F}{A}=\\frac{4F}{\\pi d^2}."

Finally,


"\\Delta l=l\\frac{\\sigma}{E}=l\\frac{F}{AE}=0.083\\text{ mm}."

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