The work of energy theorem states that an increase in net work results in what?

Air is contained in a variable-load piston-cylinder device equipped with a paddle wheel. initially, air is at 400 kpa and 17°c. the paddle wheel is now turned by an external electric motor until 75 kj/kg of work has been transferred to air. during this process, heat is transferred to maintain a constant air temperature while allowing the gas volume to triple. calculate the required amount of heat transfer in kj/kg.

Ablock of mass m slides on a horizontal frictionless table with an initial speed v0 . it then compresses a spring of force constant k and is brought to rest. the acceleration of gravity is 9.8 m/s2. how much is the spring compressed x from its natural length? 1) x = v0*sqrt(k/(mg)) 2) x=v0*sqrt(m/k) 3) x=v0*((mk)/g) 4) x=v0*sqrt(k/m) 5) x=v0*(m/kg) 6) x=v0*sqrt((mg)/k) 7) x=(v0)^2/(2g) 8) x=v0*(k/(mg)) 9) x=(v0)^2/(2m) 10) x=v0*((mg)/k)

According to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does maria's voyage take according to samir?