You just should have already derived an expression for the \"frictionless\" spee

Question

You just should have already derived an expression for the "frictionless" speed of a car in a banked turn. Now assume that the coefficient of friction is us. Find an expression for the maximum speed at which a car can drive through a turn with radius R and banking angle theta. Evaluate your answer: test whether in the two limiting cases of "no friction" and "level road" your answer will turn into the two results you already have derived for these cases. Below answer with the maximum speed (in mph) for a turn with radius 120 m, banking angle 14 degree, and coefficient of static friction 0.47.

Explanation / Answer

here,

let the mass of the car be m

moving with a speed of v at the curve curved at theta degree

the radius of the curve is r

equating the forces

m*g*sin(theta) + us*m*g*cos(theta) = m * v^2/r

when there is no friction

m*g*sin(theta) = m * v^2/r

v = sqrt( r*g*sin(theta) )

when level road or theta = 0

m*g*sin(0) + us*m*g*cos(0) = m * v^2/r

us *g = v^2/r

v = sqrt( us*r*g)

when radius , r = 120 m

theta = 14 degree

us = 0.47

the maximum speed be v

m*g*sin(theta) + us*m*g*cos(theta) = m * v^2/r

9.8 * sin(14) + 0.47 * 9.8 *cos(14) = v^2/120

v = 28.65 m/s

the maximum speed is 28.65 m/s

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