provided thrust to lift the second stage, third stage, and payload to an altitude of about 100km within the first 150 seconds of flight, at which point it experienced a maximum acceleration of38/².A Young's modulus of 73.1GPa, a yield strength of 390MPa, a density of 2840/³, and a thermal expansion coefficient of22 10⁶¹. Assume the S-IC tank structure is a smooth cylinder with an outer diameter of 10 meters, a thickness of 5.5 mm, and a height of 41 meters when nothing is mounted on top of it. The empty mass of everything above the stage is 9.7 10⁴ , and the mass of everything above the stage is 2.9 10⁶ when fully fueled. Find:

• How much the stage shrinks when the empty stages are placed atop the S-IC
• How much the stage shrinks when the vehicle is fully fueled
• How much the stage shrinks under full acceleration
• The average axial stress experienced in each of these three cases
• The factor of safety in each of these three cases

Ignore the mass of the S-IC structure itself and propellant; all we care about is how the tank has to deal with supporting the masses above it.