4.a 10- kg mass is attached to a spring, stretching it 0.7 m from its natural length. the mass is started in motion from the equilibrium position with an initial velocity of 1 m/s in the downward direction. a. find the equation of motion assuming no air resistance. b.when is the first time the mass goes through the equilibrium position after it was set in motion. c. find the equation of motion assuming air resistance equal to -90x’(t) newtons. d.what is the long term behavior of the motion described in part (c)?

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.

Ablock having mass m slides down an inclined plane. the force of friction between the block and the inclined plane is f, the block's weight is m g, and the normal force is n. (a) draw a free – body force diagram showing the forces acting on the block. (b) write down all relevant newton’s equations for a given situation.

If we decrease the amount of force and keep all other factors the same what will happen to the amount of work