In an experiment, students roll several hoops down the same incline plane. Each hoop has the same mass but a different radius. Each hoop rolls down the incline without slipping. Which of the following graphs best shows the linear speed V of the hoops at the bottom of the incline as a function of the radius r of the hoop?

When an object moves in uniform circular motion, the direction of its acceleration is a) in the same direction as its velocity vector. b) in the opposite direction of its velocity vector c) is directed toward the center of its circular path. d) is directed away from the center of its circular path. e) depends on the speed of the object.

In a steady-flow steam power plant system, two adiabatic high-pressure and low-pressure turbines ane used to generate power. superheated steam enters the high-pressure turbine at 8 mpa and 550°c. the steam expands in the high-pressure turbine to a saturated vapor at 3 mpa. in order to increase the powe generation of the power plant, another steam turbine working in a lower pressure ranges is deployed. the outlet vapor from the first turbine is heated up at a boiler to the temperature of 500 c at the constant pressure of first turbine's outlet (3 mpa). then, the vapor enters the second turbine and produces extra work. the exit conditions of the second turbine are 5o kpa and 90 percent quality. if the total power output of the power plant is 25 mw, determine a) the mass flow rate of the water (kg/s). b) heat transfer rate in the boiler (mw). (30 points) 3 mpa 00 c 8 mpa s0 c high pres turbine low pres boiler turbine 50 kpa 3 mpa 09 saturated vapor t heat engine, shown in the figure, operates between high temperature and low temperature of through a heat 4. a carnot tn and tu respectively. this heat engine receives energy from a heat reservoir at t exchanger where the heat transferred is proportional to the temperature difference as ? = k (z,-7, ). it rejects heat at a given low temperature tl. to design the heat engine for maximum work output, find the high temperature, th, as a function of tes and t. (15 points) qe

Acar moves a distance of 50.0 km west, followed by a distance of 64.9 km north what was the magnitude of the displacement of the car, in units of kilometers?