A solid sphere having a diameter d and specific weight γs is immersed in a liquid having a specific weight γf (γf > γs) and then released. It is desired to use a model system to determine the maximum height, h, above the liquid surface that the sphere will rise upon release from a depth H. It can be assumed that the important liquid properties are the density, γf/g, specific weight, γf, and viscosity, μf Establish the model design conditions and the prediction equation, and determine whether the same liquid can be used in both the model and prototype systems.

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?