At a certain point along the path in projectile motion, the projectile has a velocity v with arrow whose scalar components are vx = +30 m/s and vy = +40 m/s. as the projectile moves along the path, what would be its minimum speed?

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.

Astudent pushes on a 20.0 kg box with a force of 50 n at an angle of 30° below the horizontal. the box accelerates at a rate of 0.5 m/s2 across a horizontal floor. what is the value of the normal force on the box? 200 n 243 n 156 n 225 n

When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?