Physics rotational motion

Question

A school installs a giant rotating platform. It makes one full rotation every 14 seconds and has a radius of 12 meters.

A) What is the tangential velocity of a man if he stands on the edge of the platform?

B) If the man has a mass of 70 kg and the maximum static friction under his feet is equal to 160 Newtons, can he stay standing at the edge of the platform?

C) At what radical distance from the center of the platform would such a person be able to stand given the same friction?

Answer 1

Let

T = 14 s be the period of the platform,

m = 70 kg be the weight of the man,

F = 160 N be the force of friction,

r be the distance of the man from the center of rotation.

A)

His speed is the ratio between the distance of one rotation and the time for one rotation:

v = 2πr/T

Substituting actual numbers

v = 2π x 12m / 14s = 5.4 m/s

C)

The maximum distance r is at the point where the centrifugal force equal

the force of friction.

mv²/r = F

Replacing v by the identity from A)

m(4π²r²/T²)/r = F

4mπ²r/T² = F

r = T²F/4mπ²

Substituting actual numbers

r = 14² s² x 160 N / (4 x 70 kg x π²) = 11.3 m

B) Using the result of C) the answer is "no".