Answer to Question #106043 in Classical Mechanics for Christopher Bach Bazira

Question

A simple carousel consists of a flat circular floor that rotates about 12 seconds.

a) Calculate and illustrate all the forces acting on a person standing 4.5 m from the center of the carousel. The person weighs 55 kg.

b) What is the shortest lap time the carousel can have without the person starting to slip? The friction number between the person's shoes and the floor is 0.45.

Answer 1

a)

$$W=mg=(55)(9.8)=539\ N$$

$$F_c=m\omega^2r=mr\frac{4\pi^2}{T^2}=(55)\frac{4\pi^2}{12^2}(4.5)=68\ N$$

b)

$$r=0.5at^2=0.5\mu gt^2$$

$$4.5=0.5(0.45)(9.8)t^2$$

$$t=1.4\ s$$