Amassless spring has unstretched length l₀ and force constant k. one end is now attached to the ceiling and a mass m is hung from the other. the equilibrium length of the spring is now l₁.
(a) write down the condition that determines l₁.
suppose now the spring is stretched a further distance x beyond its new equilibrium length. show that the net force (spring plus gravity) on the mass is f = -kx. that is, the net force obeys hooke's law, when x is the distance from the equilibrium position — a very useful result, which lets us treat a mass on a vertical spring just as if it were horizontal.
(b) prove the same result by showing that the net potential energy (spring plus gravity) has the form u (x) = const + 1/2 kx².

Aregular polygon has angkes of size 150° each. how many side has the polygon

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)

Suppose a comet has an orbital period of 309.1 years around the sun. what is it’s average distance from the sun?