Question
If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 100 m radius curve banked at $15.0^\circ$. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?
1. $16.2 \textrm{ m/s}$
2. $0.234$

# OpenStax College Physics, Chapter 6, Problem 30 (Problems & Exercises)

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Hello Shaun, thank you for this helpful website! For this problem, I am wondering, at approximately (8.38 min), where you show the equations for the x-direction, why can't we just substitute mg for the normal force, cancel out the m's in all three terms, and directly solve for mu? I did this and got an answer very similar to yours, 0.235. This certainly saves a lot of algebra and substitution, but maybe it's not correct? Thank you!

Hello rhgonebirding,
Thank you for the question. It turns out that the algebra is nevertheless necessary: $F_N \neq mg$! The normal force is not directed only upwards, but rather perpendicular to the banked curve - it is $15^\circ$ off vertical. The combination of the vertical component of the normal force, plus the vertical component of friction, together offset gravity downward.
Hope this helps,
Shaun