A horizontal, uniform, copper rod has an original length 10, cross-sectional area A, Young's modulus Y, and mass m. It is supported by a frictionless pivot at its right end and by a cable at its left end. Both pivot and cable are attached so that they exert their forces uniformly over the rod's cross section. The cable makes an angle 6 with the rod and compresses it.
(a) Find the stress exerted by the cable and pivot on the rod.
(b) Find the change in length of the rod due to this stress.
(c) The mass of the rod equals pAlo, where p is the density. Show that the answers to parts (a) and (b) are independent of the cross-sectional area of the rod.
(d) The density of copper is 8900 kg/m'. Take Y for compression as given for copper in Table 11.1. Find the stress and change in length for an original length of 1.8 m and an angle of 30
(e) By how much would you multiply the answers of part (d) if the rod were twice as long?