A dense particle with mass 5 kg follows the path r(t)=⟨sin(3t),cos(4t),2t9/2⟩r(t)=⟨s in⁡(3t),cos⁡(4t),2t9/2⟩ with units in meters and seconds. What force acts on the mass at t=0t=0?

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 object a collides with object b and bounces back its final momentum is?

Frank just graduated from eighth grade. assuming exactly four years from now he will graduate from high school how many seconds does he have until his high school graduation