A string is wrapped multiple times around a massive pulley of radius 0.3 meters. A mass is attached at the free end of the string, as shown in the image above. The mass is released at t=0 seconds. Assume friction in the pulley is negligible. This pulley has a moment of inertia of 59 kg·m2. Immediately after t=0, the tension in the rope is 22 newtons. What will be the angular velocity of the pulley after 4 seconds?

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.

What was the approximate temperature of the universe at an age of 1015 s?

Let f(t) be a function on [0, infinity). the laplace transform of f is the function f defined by the integral f(s)equalsintegral from 0 to infinity e superscript negative st baseline f left parenthesis t right parenthesis dt. use this definition to determine the laplace transform of the following function.