(a) Referring to the metal rod in Figure 9.2a (under tensile stress), show that Eq. 9.4 can be rewritten to resemble a Hooke’s law type of spring relationship for the rod. That is, show that it can be written as F = k ∆L, where k is the “effective” spring constant for the rod. Express k symbolically in terms of the rod’s cross-sectional area A, its Young’s modulus Y, and its unstressed length Lo and show that it has the proper SI units.
(b) Now consider a thin rod of iron that is subjected to a tensile force of 2.00 x 103N. If it has a cross-section of radius 1.00 cm and an unstressed length of 25.0 cm, determine its effective spring constant.
(c) By how much does this rod stretch when this force is applied?
(d) How much work is done by this stretching force?