Answered: A cat dozes on a stationary…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter7: Rotational Motion And Gravitation

Section: Chapter Questions

Problem 27P: An air puck of mass m1 = 0.25 kg is tied to a siring and allowed to revolve in a circle of radius R...

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A cat dozes on a stationary merry-go-round, at a radius of 4.9 m from the center of the ride. Then the operator turns on the ride and brings it up to its proper turning rate of one complete rotation every 6.8 s. What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding?

Expert Solution

Step 1

Radius,(r)=4.9 m ------(1) [Given]

Time of rotation,(T)=6.8 sec ------(2) [Given]

Acceleration due to gravity,(g)=9.81 m/sec² ------(3) [Universal Constant]

Suppose (F_S) be the static friction force for which the coefficient of static friction be ( $μ_{S}$ ) between the cat and the merry-go-round that will allow the cat to stay in place without sliding which is given by:-

$F_{S} = μ_{S} m g$ -----(4) [Here m is the mass]

$F_{S} = \frac{m v^{2}}{r}$ -----(5) [Here v is the velocity]

Equating (4) & (5) together we get,

$μ_{S} m g = \frac{m v^{2}}{r}$

$μ_{S} g = \frac{v^{2}}{r}$ -------(6)

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