You are testing a new roller coaster ride in which a car of mass m moves around a vertical circle of radius r. in one test, the car starts at the bottom of the circle (point a) with initial kinetic energy ki. when the car reaches the top of the circle (point b), its kinetic energy is ki/4, and its gravitational potential energy has increased by ki/2. what was the speed of the car at point a, in terms of g and r?

Two kilograms of air within a piston–cylinder assembly executes a carnot power cycle with maximum and minimum temperatures of 800 k and 300 k, respectively. the heat transfer to the air during the isothermal expansion is 60 kj. at the end of the isothermal expansion the volume is 0.4 m3. assume the ideal gas model for the air. determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kj.