Two masses m 1 and m 2 move i n a plane and interact by a potential energy U (r) = f kr 2 • Write down their Lagrangian in terms of the CM and relative positions R and r , and find the equations of motion for the coordinates X, Y and x, y. Describe the motion and find the frequency of the relative motion.

Acave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 11.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.80 m/s; (b) he is then lifted at the constant speed of 4.80 m/s; (c) finally he is decelerated to zero speed. how much work is done on the 78.0 kg rescue by the force lifting him during each stage

Calculate the velocity of a car traveling in a straight path due east with a distance of 16 meters in 2 seconds. question 1 options: a)32 m/s b)32 m/s e c) 8 m/s e d) 8 m/s

Complete these sentences. if a roller coaster train has a potential energy of 1,500 j and a kinetic energy of 500 j as it starts to travel downhill, its total energy isj. once the roller coaster train gets closer to the bottom of the hill, its kinetic energy increases to 1,100 j, and its potential energy decreases to j. when the train reaches the bottom of the track and is traveling along the ground, its kinetic energy isj.