A power cable of copper is stretched straight between two fixed towers. If the temperature decreases, the cable tends to contract; the amount of contraction for a free copper cable is 0.0017% per degree celsius. Show that the stretched cable will snap if its temperature decreases by 128°C.Ignore the weight of the cable and assume Hooke's law is obeyed until the cable breaks. Young's modulus for copper is 11.0 x 10^10 N/m^2 and the ultimate tensile strength of copper is 2.4 x 10^8 N/m^2.
Change in length=(coefficient of expansion)(original length)(change T)= (.0017)(chose your favoret length, I chose 100)( -128 because T is decreeing)=-21.76 Strain = (change in length)/(original length)= 21.76/100= .2176Pa (for simplicity's sake I dropped the negative, rember the wire is in tension) Stress = (youngs modulus)(strain)= (11?10^10)(.2176)= 2.3936?10^10 Pa The UTS (2.4?10^8)<(2.39?10^10) so there is definitely necking and because of the difference most likely there was failure long ago.
