Banked Curve: Finding the normal force with friction

[WitteVrouw]

This is a five part question, of which I have completed 2 parts, which I will explain below. This is a level 1 physics problem concerning centripetal motion on banked curves and the forces that apply to objects in these scenarios.


PROBLEM:

A car travels at a speed of 27m/s around a curve with a radius of 43m (keep in mind that acceleration due to gravity is 9.8m/s²

What is the net centripetal force needed to keep the car from skidding sideways?
Answer in units of N.


38,993.02326N My solution to part one ----> Correct


Were there no friction between the car's tires and the road, what centripetal force could be provided just by the banking of the road?
Answer in units of N.

15,782.67791N My solution to part two ------> Correct


Now suppose the friction force is sufficient to keep the car from skidding. Calculate the magnitude of the normal force (Fn) exerted on the car by the road's surface. Hint: Check the correctness of your answer to the first part before proceeding with this and the following questions.

Solution to Part three -------> Unknown

Calculate the magnitude of the friction force.
Answer in units of N.

Solution to Part four ---------> Unknown


Calculate the lowest possible value of the static friction coefficient mu_s that would prevent the car from skidding.

Solution to Part five ---------> Unknown

NOW, here is where I am stuck. I am fairly sure that parts 3-5 deal with the components of the Normal Force and the Force of Static Friction but I keep getting lost with my equations (somehow I end up with far too many sin-cos-tan arrangments with Fn, etc, divided by one another).

SO,

Here is my data so far:

Fc (centripetal force) needed to keep car from skidding sideways: 38,993.02326N
Fc provided by just the banking of road (without friction): 15,782.67791N
Magnitude of Normal Force: Unknown
Magnitude of Ff (friction force): Unknown
Static friction coefficient mu_s: Uknown
Mass of car: 2300kg
Radius: 43m
Ac (centripetal acceleration): 16.95348837m/s²
Velocity: 27m/s
Angle of Incline: 35 degrees

Help would be so greatly appreciated! Sorry to inconvenience anyone, I know the problem is quite extensive! Thank you very much!

 

[kuruman]

You can organize your equations better with a free body diagram. Did you draw one for the banked turn? I suggest that you resolve the forces along vertical and horizontal axes in the banked turn case. Note that the vertical component of normal force must be equal to the weight whilst the horizontal component provides the centripetal acceleration required to negotiate the turn.

 

[Delta2]

The presence of friction complicates things. I think the system of two equations by resolving forces in horizontal and vertical components are
$$F_N\cos 35-mg-T\sin 35=0$$
$$F_N\sin 35+T\cos 35=F_C$$ where $F_C$ the answer in first question.

 

[haruspex]

but I keep getting lost with my equations

We can help with that, but only if you show us your working so far.