If a sum of money triples in a certain period of time at a given rate interest, compute the value of the single payment present worth factor

A 2.5” diameter by 2 in. long journal bearing is to carry a 5500-lb load at 3600 rpm using SAE 40 lube oil at 200°F through a single hole at 25 psi. Compute the bearing pressure.

A high alloy spring having squared and ground ends and has a total of 16 coils and modulus of elasticity in shear of 85 GPa. Compute the Wahl factor. The spring outside diameter is 9.66 cm and wire diameter is 0.65 cm.

Saturn V First-Stage Structural Analysis The first stage of the Saturn V (also called the S-IC) 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 of 38𝑚/𝑠2 . The first stage structure (the shell around the propellant tanks) transmitted the force produced by the engines to the upper stages through its outer skin. This skin was composed of 2219-T87 aluminum, which has a Young's modulus of 73.1GPa, a yield strength of 390MPa, a density of 2840 𝑘𝑔/𝑚3 , and a thermal expansion coefficient of 22 ∗ 10-6𝐾-1 . We will perform an analysis of the S-IC structure and the loads it carried through a series of scenarios. The exception is for Part 5, which must be done by hand as it requires significant drawing and only uses symbolic variables, no numerical calculations. I also recommend setting up the equations for Part 4 by hand and then using the .m file to perform the actual computations. 

Part 1: 

 The S-IC stage shell was required to support the load of the second stage, third stage, instrument unit, and Apollo spacecraft modules, both on the pad and during launch. The maximum mass it had to support was when the fully-fueled vehicle was sitting on the pad, and the maximum acceleration it experienced was immediately before stage burnout (when the S-IC was empty but all the other stages were full). 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 𝑘𝑔, and the mass of everything above the stage is 2.9 ∗ 106 𝑘𝑔 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.

Part 2: 

 In reality, the stage did not have a uniform cross section; it was composed of steps of decreasing thickness toward the top of the S-IC, to save structural mass. Suppose the tank wall thickness decreased from 6.5 mm at the bottom to 4.3 mm at the top in eight steps of equal height. Each of the eight "rings" would have a constant wall thickness, the same height as the other rings, and the total height of the stage would still be 41 meters. Repeat the first three bullet points from Part 1, to find how much the stage will contract with the stepped cross sections instead of the uniform. Additionally, find the mass savings by constructing the tank in this manner.

Part 3: 

If the 41m height measurement given in Part 1 was taken at an ambient temperature of 25C, how much would the entire S-IC shrink due to thermal contraction (with no load atop the stage) at an operating temperature of -100C? You may choose either the uniform or stepped cross-section configuration from Part 1 or Part 2 to solve this problem, but there is one optimal solution within the scope of this project. Explain which option you chose and why.