# Problem: A smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.00  m/s. After one revolution, its speed has dropped to 6.00 m/s because of friction with the floor.(a)  Find the energy transformed from mechanical to internal in the particle–hoop– floor system as a result of friction in one revolution.(b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.

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###### Problem Details

A smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.00  m/s. After one revolution, its speed has dropped to 6.00 m/s because of friction with the floor.

(a)  Find the energy transformed from mechanical to internal in the particle–hoop– floor system as a result of friction in one revolution.
(b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.