Finding max velocity for a kart on a circular, banked track

[PhysicsNoob2]

Homework Statement

You create a banked track of 12 degrees, now what's the maximum linear velocity?
And how would this change if a child was driving the kart instead?

Relevant Equations

F=mv^2/r
F=mg sin(theta)

This is a UK A-Level question that I'm really struggling with, and can't seem to find any resources online that explain it well.

I've been given the following details:
mass of gokart + driver = 520kg
radius of track = 42m
Maximum frictional force between tyres and road on flat track F = 20% weight of kart+driver (104kg)
Bank of track = 12 degrees

And I've calculated the following in earlier questions:
Coefficient of friction = F/N = 0.0204
Angular velocity (Flat track) w = sqrt (F/mr) = 0.069 rad/s
Linear velocity (Flat track) v = sqrt (Fr/m) = 2.898 m/s

Here is my working out for the question I'm stuck on so far:
F (Force down the slope) = mg sin (theta)
F = 520 * 9.8 * sin(12)
F = 1059.51...

v = sqrt (Fr/m)
v = sqrt (1059.51... * 42 / 520)
v = 9.25 m/s (2dp)

I'm certain that I'm doing something wrong here, as this is using the force down the slope and not the centripetal force towards the centre of the track. But I've never seen anywhere that shows me how to calculate this? Or have I got this right and am worrying about nothing?

And when calculating a lighter kart (Taking in to account the child driving), I get the same maximum linear velocity. Is this correct? As intuition would suggest that the kart would move faster with a child in it than with an adult?

Thanks in advance

 

[kuruman]

You need to draw a free body diagram (FBD) of the car as it goes around the circle. Note that the circle is horizontal which means that the net force on the car is horizontal. You are correct in that you should not use the downslope force as the centripetal force. Also, you completely ignored the force of static friction between the tires and the incline. It, also, has a horizontal component that contributes to the centripetal acceleration.

 

[PhysicsNoob2]

Yeah I've realised that I've made some big mistakes on the earlier bits (For example used mass rather than weight for the coefficient of friction calculations), so I'm going to go back and start again. I think I've got the idea now anyway, thanks for the pointers and I'll see how I get on! :)