Calculating Apparent Weight on a Rotor Ride

[LesterTU]

Homework Statement

A 30-kg child is on a rotor ride at a carnival. The radius of the rotor is 3 m and it completes 0.4 revolutions in one second. The coefficient of static friction is 0.6. What is the magnitude of the child's apparent weight?

Homework Equations

ΣF_x : F_N = mv²/r
ΣF_y : F_f = F_g

The Attempt at a Solution

First I need to find v:
0.4 revolutions per second is equivalent to one revolution per 2.5 s, so T = 2.5 s.
v = 2πr / T => v = 7.54 m/s.

Since the apparent weight is the magnitude of the resultant force exerted on a body by a supporting surface, the way I see it F_N is the only force that fits this description so I figured
apparent weight = F_N = mv²/r = 568.5 N.

However the solution given by the author says that
apparent weight = (F_N² + F_g²)^1/2 = 640 N.

I've been trying to understand why mg plays a role in the child's apparent weight but I don't see how in this case

 

[TSny]

Hello and welcome to PF!

Are you sure that F_N is the only force exerted on the person by the wall? Consider the forces shown in your figure.

 

[LesterTU]

Thanks!

I guess the friction applies in this case but for some reason because of its direct relationship with the normal force I didn't consider it. It makes a lot of sense though now that I think about it

 

[TSny]

OK, good.