Astate of stress that occurs at a point on the free surface of the of a solid body is σ x= 50 mpa , σ y =10 mpa , and τxy = −15 mpa xy τ .a. evaluate the two principal normal stresses and the one principal shear stress that can be found by coordinate system rotations in the x-y plane and give the coordinate system rotations. b. determine the maximum normal stress and the maximum shear stress at this point. c. sketch the rotations and stress magnitudes

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?

Agas is compressed from vi 0.3 m, p 1 bar to of v2 0.1 m3, p2--3 bar. pressure and volume are related linearly during the process. for the gas, find the work, in kj.

Acircular aluminum shaft mounted in a journal is shown. the symmetric clearance gap between the shaft and journal is filled with sae 10w-30 oil at t 30°c. the shaft is caused to turn by the attached mass and cord. develop and solve a differential equation for the angular speed of the shaft as a function of time.