An object of mass M is attached to a string of negligible mass and spun in a vertical circle of radius R, as shown in the figure provided. As the object's height increases, its speed decreases such that the object-Earth-object's total mechanical energy remains constant. By how much does the object's kinetic energy decrease in moving from point O, the lowest point on the circle, to point P, the highest point on the circle? Justify your answer using physics fact(s) and/or theorem(s).
Expected 2MgR

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As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.

If the ama of the inclined plane below is 2, calculate the ima and efficiency. ima = efficiency =

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