Curve Speed & Inclines

[NA19]

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The question diagram is attached. The actual question is:

Which of the following would require the bank angles which currently exist on highways to be increased?
a) The average mass of vechicles on the high way increases.
b) The average mass of vehicles on the highway decreases.
c) Curve speed limits are increased.
d) Curve speed limits are decreased.

I was thinking that this has something to do with the downward force on the incline and making sure that the car doesn't slide down the incline. Changing the mass or curve speed limits may cause the car to slide down the incline but I'm not sure how this makes sense mathematically. And so, I'm trying to understand the mathematical explanation.

My answer key says the answer is C.
(this is from examkrackers)

 

[Patassa]

The question diagram is attached. The actual question is:

Which of the following would require the bank angles which currently exist on highways to be increased?
a) The average mass of vechicles on the high way increases.
b) The average mass of vehicles on the highway decreases.
c) Curve speed limits are increased.
d) Curve speed limits are decreased.

I was thinking that this has something to do with the downward force on the incline and making sure that the car doesn't slide down the incline. Changing the mass or curve speed limits may cause the car to slide down the incline but I'm not sure how this makes sense mathematically. And so, I'm trying to understand the mathematical explanation.

My answer key says the answer is C.
(this is from examkrackers)

This is one of the less intuitive questions in this material, the "believe it or not" types. The tendency is to believe that a heavier car going at the same speed of a lighter one will be harder to keep on the less steep grade. Cars won't slide down the incline, they might go too fast and fly off of it though, that the purpose of banking curves. Think nascar.

Fc = Ff so mass cancels out. It only depends on speed, where Fc = centripetal force = m v^2/r and Ff = mg cos theta uk , m cancels out and you can solve for the velocity. everything will be constant for every other car given the same tires (friction coefficient).

Hope this helps.