Question

A baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle ((r = 15.0 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.980, and the angle θ is 19.0°. How much time is required for your suitcase to go around once? Assumme that the static friction between the suitcase and the carousel is at its maximum.

Answer 1

Give
  
   circle of radius r = 15 of a carousel

the coefficient of kinetic friction is mue k = 0.980, and the slope is θ is 19.0°

here the centripetal force equal to the frictional force

   mv^2/r = muek* mg cos theta

from relation v = r*w,

   m W^2*r^2/r = muek *mg*cos theta

   W = sqrt((mue k*g*cos theta)/(r))

   W = sqrt(0.98*9.8*cos 19/15)

   W = 0.7780 rad/s

time period is T = 2pi/W = 2pi/0.7780 = 8.076 s

so time required for your suitcase to go around once is 8.076 s