Consider, for instance, a bar of initial length L and cross-sectional area A str

Question

Consider, for instance, a bar of initial length L and cross-sectional area A stressed by a force of magnitude F. As a result, the bar stretches by ?L. (Figure 1)

Let us define two new terms:

stress=FA.

strain=?LL.

It turns out that the ratio of the tensile stress to the tensile strain is a constant as long as the tensile stress is not too large. That constant, which is an inherent property of a material, is called Young's modulus and is given by

Y= F/A?L/L.

a) What is the SI unit of Young's modulus?

b) Consider a metal bar of initial length L and cross-sectional area A. The Young's modulus of the material of the bar is Y. Find the "spring constant" k of such a bar for low values of tensile strain.

Express your answer in terms of Y, L, and A.

c) Ten identical steel wires have equal lengths L and equal "spring constants" k. The wires are connected end to end, so that the resultant wire has length 10L. What is the "spring constant" of the resulting wire?

Option1) 0.1k

Option 2) k

Option3) 10k

Option4) 100k

d) Consider a steel guitar string of initial length L=1.00m and cross-sectional area A=0.500mm2. The Young's modulus of the steel is Y=2.0

Explanation / Answer

a)N/m2

b)Y=(F/A)/(l/L)

Y= (F/l) * (L/A)

k = YA/L

c) 0.1k

d)2*10^11 = (1500/0.5*10^-6) /(l/1)

l=0.015m =15mm

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