The material selected for the shaft design has an ultimate tensile strength, Sut, of 68 kpsi and a yield strength, Sy, of 57 kpsi. Determine the location of the critical section on the shaft. (You must provide an answer before moving to the next part.)

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Apiping systems consists of 6 m of 6-std type k and 12 m of 4-std type k, both drawn copper tubing. the system conveys ethylene glycol at a rate of 0.013 m3/s. the pressure drop across the system is to be calculated. there are two 90° elbows in the 6-in pipe, a reduction from the 6-in pipe to the 4-in pipe and four 90° elbows in the 4-in pipe. all fittings are soldered (same as flanged) and regular. the inlet and outlet of the system are at the same height.

Acubic shaped box has a side length of 1.0 ft and a mass of 10 lbm is sliding on a frictionless horizontal surface towards a 30 upward incline. the horizontal velocity of the box is 20 ft/s. determine how far up the incline the box will travel (report center of mass distance along the inclined surface, not vertical distance)