You are testing a new roller coaster ride in which a car of mass mm moves around a vertical circle of radius RR. In one test, the car starts at the bottom of the circle (point A) with initial kinetic energy KiKi. When the car reaches the top of the circle (point B), its kinetic energy is Ki/4Ki/4, and its gravitational potential energy has increased by Ki/2Ki/2. What was the speed of the car at point A, in terms of gg and RR?

Suppose a force of 60 n is required to stretch and hold a spring 0.1 m from its equilibrium position. a. assuming the spring obeys hooke's law, find the spring constant k. b. how much work is required to compress the spring 0.5 m from its equilibrium position? c. how much work is required to stretch the spring 0.6 m from its equilibrium position? d. how much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. kequals 600