Physics-Speeds limits, bank angles, and radii of curvature

[sniderwes]

So the answer given is B, and I understand why. But isn't A also false? An increased radius of curvature would decrease the bank angle, which would require a lower speed limit.

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[inasensegone]

The bank angle and the radius of curvature are 2 SEPARATE ways to allow for the increase in the speed limit. Increasing the bank angle provides a greater amount of friction. Increasing the radius of curvature (think of driving around a 5 mile circle vs doing donuts in a parking lot) will allow for a greater speed limit because the rate of change in direction (acceleration) toward the center of the circle is smaller and so the chances of you losing control are reduced. It's like driving on the freeway and changing lanes gradually as opposed to cranking the wheel and changing lanes suddenly (which could cause you to lose control).

EDIT:
I originally said "Increasing the bank angle provides a greater coefficient of friction" But I meant to say provides a greater amount of friction. The coefficient is a constant for a given material.

 

[sniderwes]

The bank angle and the radius of curvature are 2 SEPARATE ways to allow for the increase in the speed limit. Increasing the bank angle provides a greater coefficient of friction. Increasing the radius of curvature (think of driving around a 5 mile circle vs doing donuts in a parking lot) will allow for a greater speed limit because the rate of change in direction (acceleration) toward the center of the circle is smaller and so the chances of you losing control are reduced. It's like driving on the freeway and changing lanes gradually as opposed to cranking the wheel and changing lanes suddenly (which could cause you to lose control).

So when they say "a smaller radius of curvature leads to a greater bank angle," they are assuming velocity is held constant...in which case a greater bank angle must make up for the smaller radius.

Man...you're really good at physics! You helped me with that other question too. You'd better get a 15 😉

 

[inasensegone]

So when they say "a smaller radius of curvature leads to a greater bank angle," they are assuming velocity is held constant...in which case a greater bank angle must make up for the smaller radius.

Man...you're really good at physics! You helped me with that other question too. You'd better get a 15 😉

In answer, B, they say the bank angle increases with radius of curvature. This would seem to imply that the 2 are co-dependent which is false. If you increase the bank angle, you have increased the amount of friction and therefore you don't have to increase the radius of curvature (as much or at all)

Now take a look at answer D, which may be why you're confused: A smaller radius of curvature leads to a greater bank angle. If you have a smaller radius of curvature, you're making a tight turn in the car (small radius = small circle). In order to allow you to do this at highway speeds, you need to increase the amount of friction.

This is all relating to centripetal force (F=mv^2/r)... when you travel in a circle, you need a centripetal force that is directed toward the center of the circle. This centripetal force is what keeps you moving in a circle and prevents you from going straight. This force must be supplied by something = friction. With a large radius of curvature you have sufficient friction from the pavement and the tires to keep traveling in a circle. With a tight turn, you need more, hence the bank angle.

Haha thanks... I'm decent at physics. When I started my content review, physics was my biggest weakness. I owe a lot of my proficiency to TBR.