Tainless steel (AISI 304) ball bearings, which have uni- formly been heated to 850C, are hardened by quench- ing them in an oil bath that is maintained at 40C. The ball diameter is 20 mm, and the convection coefficient associated with the oil bath is 1000 W/m2 K. (a) If quenching is to occur until the surface tempera- ture of the balls reaches 100C, how long must the balls be kept in the oil? What is the center tempera- ture at the conclusion of the cooling period? (b) If 10,000 balls are to be quenched per hour, what is the rate at which energy must be removed by the oil bath cooling system in order to maintain its temper- ature at 40C?

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?