Problem 1: A person walks with constant speed v, in a circular path of radius R

Question

Problem 1: A person walks with constant speed v, in a circular path of radius R = 4.00 m on a carousel rotating with a constant angular speed of 3 revolutions per minute. The circular path is concentric with the center of the carousel. If the mass of the person is m = 60.0 kg and the coefficient of stantic frienction with the surface of the carousel is Hs 0.300, how fast, relative to the carousel, can the person walk before he/she starts to slip if he/she goes: a) in the direction of the rotation? b) opposite to the direction of rotation? (Hint: You have to carefully consider the acceleration in the carousel frame a', in addition to any inertial/fictitious forces. Also assume that g = 9.80 m/s2)

Explanation / Answer

speed of person = v'

radius of circular path, R = 4 m

angular speed of carousel, w = 3 rpm = 0.314159 rad/s

mass of person, m= 60 kg

coefficeint of static friciton, k = 0.3

a. in the direction of the rotation, let max speed be v'

then

(v' + wR)^2/R = kg

v' = sqroot(kRg) - wR = sqroot(0.3*4*9.81) - 0.314159*4 = 2.17439 m/s

b. in the opposite direction

v' = sqroot(kRg) + wR = sqroot(0.3*4*9.81) + 0.314159*4 = 4.68767 m/s

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