Answer:
μ = 0.604
Explanation:
For the cat to stay in place on the merry go round, the maximum static frictional force must be equal in magnitude to that of the centripetal force.
Now, Centripetal force is given as;
Fc = mv²/r
Where r is radius and v is tangential speed and m is mass.
We also know that maximum static frictional force is given by;
F_static = μmg
Where μ is coefficient of friction
Now, equating both forces, we have;
mv²/r = μmg
Divide through by m;
v²/r = μg
Now, tangential speed can be expressed as;
v = circumference/period
Thus, v = 2πr/T
Where T is period of rotation and
2πr is the circumference of the merry go round.
Thus,
v²/r = μg is now;
(2πr/T)²/r = μg
Making μ the subject, we have;
(2πr/T)²/rg = μ
μ = [(2π x 5.4)/6]²/(5.4 x 9.8)
μ = 0.604