Two racing cars apprach a turn. Car A is in the inside lane and car B is in the outside lane. The two cars travel through the turn at a constant speed. Just before the turn the two cars are side by side.
a)If the friction coefficient is infinite, which car will be ahead at the end of the turn?
b)Consider now the friction coefficient for the tires on the asphalt. Which car is ahead after the turn?
The Attempt at a Solution
First off this may seem like a intro physics question, and it kind of is, but its from my classical mechanics class and the semester just started, so this is kind of a "review" of elementary Newtonian mechanics.
For part a), I said that Car A would be ahead after the turn, because it can travel the same speed as Car B, and has less distance to travel. I think this is right.
For part b, I am not sure. We asked our professor in class if the angle of the turn or the width of the lanes had anything to do with it and he said "no, there is a way to show which car would end up ahead".
I am not sure how to show this. Wouldn't car A still be ahead? It says that the two cars travel through the turn at constant speed, and that they are side by side. I guess this doesn't imply that they are traveling at the same constant speed through the turn. I don't know how slow A would have to go on asphalt compared to B due to the tighter turn it would have to make. Intuitively, A would have to go slower, but at the same time has less distance to travel, and B could go faster with more distance to travel. How is there a way to know with only the information given?