Torque with constant circular velocity

[Matejxx1]

Homework Statement

a passenger with height 175cmis driving on a city bus. The center of mass is at h=110cm above the middle point of the shoe which are 30 cm long. The passenger is standing in the direction of the ride.
h=175cm
h*=110cm
shoe size = 30 cm

b)
the bus is driving in a circle which has the radius of 20m with a constant speed of 20 km/h.For what angle relative to the vertical axis should the passenger lean so that he/she would not tip over.

Homework Equations

F_c=m*v²/r
F_n=m*g*cosα
F_x=m*g*sinα

The Attempt at a Solution

So here is what I tried to do
f_c=m*(20/3,6)²/20..... I got F_c=1,543m
and here is something I don't understand. Since the centripetal force is acting toward the center of the circle, why is it incorrect to just use the F_x component of m*g
I tried doing it like this
F_c=1,543m F_x=m*g*sinα...since the body is not moving Torque=0
1,543m=m*g*sinα
sinα=(1.543*m)/(m*g) the masses cancel out
sin=1.543/9.8
sinα=0,157
α=9.05°
which is incorrect. The right answer is 8.9° and the end equation should look like this
tanα=v²/(r*g)
Can someone please explain or help me get to this equation tanα=v²/(r*g) [/b]
Thank you for reading

 

[Simon Bridge]

So here is what I tried to do
f_c=m*(20/3,6)²/20..... I got F_c=1,543m

Are you given the mass of the passenger?
What are the units for F_c?

...and here is something I don't understand. Since the centripetal force is acting toward the center of the circle, why is it incorrect to just use the F_x component of m*g

... you mean the horizontal component of the weight?
Cartesian coordinates don't make a lot of sense here.

I tried doing it like this
F_c=1,543m F_x=m*g*sinα...since the body is not moving

... but the body is moving - in fact, for the term "centripetal force" to make sense, it must be accelerating: i.e. moving in a circle. So it must be acted on by an unbalanced force.

If I read you correctly, you tried to arrange to have zero horizontal force.

In the inertial frame, the net force on the body must point horizontally towards the center of the turn and sufficient to maintain circular motion. There should be zero net torque as well because the body has zero angular acceleration - it is rotating because it is constantly oriented along the axis of the turning bus.