A 2.7-meter-tall, 0.40-meter (cross section) radius column is designed to suppor

Question

A 2.7-meter-tall, 0.40-meter (cross section) radius column is designed to support a 5.0x10° N load. One wants for the column not to compress more than 0.0016 meters (1.6 mm) while supporting that load. a) What may be the smallest Young modulus of the material the column is made of? That is to say, what is the Young modulus of the column, if it is compressed by 0.0016 m while supporting a 5.0x10° N load? b) If we model the column as a (massless) spring, what would be its spring constant? Present your answers with the precision of two significant figures

Explanation / Answer

a] Youngs modulus Y = stress/strain

= [F/A]/[deltaL/L]

= [ 5e6/(pi*0.4^2)] / [ 0.0016/2.7]

= 1.7*10^10 Pa answer

b] for spring, F = kx

spring constant k = F/x = 5e6/0.0016

k = 3.1 *10^9 N/m answer

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