A long rod hangs straight down from one end. How long (in meters) can the rod be before its weight causes it to break off at the end if it is made of iron? titanium? Give your answer in meters.
Use the following values for densities and tensile strengths:
The densities of iron and titanium are 7.8×103 kg/m3 and 4.5×103 kg/m3 respectively.
The breaking - ultimate tensile strength: 350 MPa for iron and 450 MPa for titanium (MPa = 106 N/m2)
LFe=
LTi=
mass = rho pi r^2 L
weight = m g = rho pi r^2 L g
tensile stress at top = weight/pi r^2
= rho L g
so for iron
350 * 10^6 = 7.8*10^3 * L * 9.81
so
L = 4.57* 10^3 = 4,570 meters long
and for titanium
450 * 10^6 = 4.5*10^3 * L * 9.81
so
L = 10.2*10^3 = 10,200 meters long